Algebra : some current trends : proceedings of the 5th National School in Algebra held at Varna, Bulgaria, Sept. 24-Oct. 4, 1986 / / L. L. Avramov, K.B. Tchakerian, editors |
Edizione | [1st ed. 1988.] |
Pubbl/distr/stampa | Berlin : , : Springer-Verlag, , [1988] |
Descrizione fisica | 1 online resource (XII, 248 p.) |
Disciplina | 512.9 |
Collana | Lecture notes in mathematics |
Soggetto topico | Algebra |
ISBN | 3-540-45994-4 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Matrix factorizations of homogeneous polynomials -- Some new results in the combinatorial theory of rings and groups -- On representations of infinite groups -- Integral manifolds, harmonic mappings, and the abelian subspace problem -- Valuations on ree fields -- Standard bases and homology -- Semisimple superalgebras -- On the laws of finite dimensional representations of solvable lie algebras and groups -- Lie groups and ergodic theory -- Galois theory of databases -- On the codimensions of matrix algebras -- Homology of free loop spaces, cyclic homology and non-rational poincare-betti series in commutative algebra -- Incomplete sums and two applications of Deligne's result -- Eigenvalues of matrices of complex representations of finite groups of lie type -- Normal fitting classes of groups and generalizations -- On the nilpotency of nil algebras. |
Record Nr. | UNISA-996466638403316 |
Berlin : , : Springer-Verlag, , [1988] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. di Salerno | ||
|
Algebra & trigonometry / / Michael Sullivan |
Autore | Sullivan Michael |
Edizione | [Ninth edition, Pearson new international editon.] |
Pubbl/distr/stampa | Harlow, England : , : Pearson, , 2014 |
Descrizione fisica | 1 online resource (1,118 pages) : illustrations, tables |
Disciplina | 512.9 |
Soggetto topico |
Algebra
Algebra - Study and teaching (Higher) Trigonometry Trigonometry - Study and teaching (Higher) |
ISBN | 1-292-03739-3 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Cover -- Table of Contents -- 1. Equations and Inequalities -- 2. Graphs -- 3. Functions and Their Graphs -- 4. Linear and Quadratic Functions -- 5. Polynomial and Rational Functions -- 6. Exponential and Logarithmic Functions -- 7. Trigonometric Functions -- 8. Analytic Trigonometry -- 9. Applications of Trigonometric Functions -- 10. Polar Coordinates -- Vectors -- 11. Analytic Geometry -- 12. Systems of Equations and Inequalities -- 13. Sequences -- Induction -- the Binomial Theorem -- Appendix: Graphing Utilities -- Useful Mathematical Information -- Review -- Prepare for Class "Read the Book -- Practice "Work the Problems -- Review "Study for Quizzes and Tests -- Index. |
Altri titoli varianti | Algebra and trigonometry |
Record Nr. | UNINA-9910153124503321 |
Sullivan Michael | ||
Harlow, England : , : Pearson, , 2014 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Algebra 2 [[electronic resource] ] : Linear Algebra, Galois Theory, Representation theory, Group extensions and Schur Multiplier / / by Ramji Lal |
Autore | Lal Ramji |
Edizione | [1st ed. 2017.] |
Pubbl/distr/stampa | Singapore : , : Springer Singapore : , : Imprint : Springer, , 2017 |
Descrizione fisica | 1 online resource (XVIII, 432 p.) |
Disciplina | 512.9 |
Collana | Infosys Science Foundation Series in Mathematical Sciences |
Soggetto topico |
Matrix theory
Algebra Associative rings Rings (Algebra) Commutative algebra Commutative rings Nonassociative rings Group theory Number theory Linear and Multilinear Algebras, Matrix Theory Associative Rings and Algebras Commutative Rings and Algebras Non-associative Rings and Algebras Group Theory and Generalizations Number Theory |
ISBN | 981-10-4256-X |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Chapter 1. Vector Space -- Chapter 2. Matrices and Linear Equations -- Chapter 3. Linear Transformations -- Chapter 4. Inner Product Space -- Chapter 5. Determinants and Forms -- Chapter 6. Canonical Forms, Jordan and Rational Forms -- Chapter 7. General Linear Algebra -- Chapter 8. Field Theory, Galois Theory -- Chapter 9. Representation Theory of Finite Groups -- Chapter 10. Group Extensions and Schur Multiplier. |
Record Nr. | UNINA-9910254274803321 |
Lal Ramji | ||
Singapore : , : Springer Singapore : , : Imprint : Springer, , 2017 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Algebra 4 : lie algebras, Chevalley groups, and their representations / / Ramji Lal |
Autore | Lal Ramji |
Pubbl/distr/stampa | Singapore : , : Springer, , [2021] |
Descrizione fisica | 1 online resource (332 pages) |
Disciplina | 512.9 |
Collana | Infosys Science Foundation Series |
Soggetto topico |
Algebra
Àlgebra Llibres de text |
Soggetto genere / forma | Llibres electrònics |
ISBN | 981-16-0475-4 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Intro -- Preface -- Contents -- About the Author -- Notations -- 1 Lie Algebras -- 1.1 Definitions and Examples -- 1.2 Universal Enveloping Algebras: PBW Theorem -- 1.3 Solvable and Nilpotent Lie Algebras -- 1.4 Semi-Simple Lie Algebras -- 1.5 Extensions of Lie Algebras and Co-homology -- 2 Semi-Simple Lie Algebras and Root Systems -- 2.1 Root Space Decomposition -- 2.2 Root Systems -- 2.3 Dynkin Diagram and the Classification of Root Systems -- 2.4 Conjugacy Theorem, Existence and Uniqueness Theorems -- 3 Representation Theory of Lie Algebras -- 3.1 Theorems of Ado and Iwasawa -- 3.2 Cyclic Modules and Weights -- 3.3 Characters and Harish-Chandra's Theorem -- 3.4 Multiplicity Formulas of Weyl, Kostant, and Steinberg -- 4 Chevalley Groups -- 4.1 Classical Linear Groups -- 4.2 Chevalley Basis -- 4.3 Chevalley Groups -- 4.4 Twisted Groups -- 5 Representation Theory of Chevalley Groups -- 5.1 Language of Representation Theory -- 5.2 Representations of Sn, and of GL(2.q) -- 5.3 Steinberg Characters -- 5.4 Principal and Discrete Series Representations -- 5.5 Deligne-Lusztig Generalized Characters -- Appendix Bibliography -- -- Index. |
Altri titoli varianti | Algebra four |
Record Nr. | UNISA-996466559403316 |
Lal Ramji | ||
Singapore : , : Springer, , [2021] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. di Salerno | ||
|
Algebra 4 : lie algebras, Chevalley groups, and their representations / / Ramji Lal |
Autore | Lal Ramji |
Pubbl/distr/stampa | Singapore : , : Springer, , [2021] |
Descrizione fisica | 1 online resource (332 pages) |
Disciplina | 512.9 |
Collana | Infosys Science Foundation Series |
Soggetto topico |
Algebra
Àlgebra Llibres de text |
Soggetto genere / forma | Llibres electrònics |
ISBN | 981-16-0475-4 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Intro -- Preface -- Contents -- About the Author -- Notations -- 1 Lie Algebras -- 1.1 Definitions and Examples -- 1.2 Universal Enveloping Algebras: PBW Theorem -- 1.3 Solvable and Nilpotent Lie Algebras -- 1.4 Semi-Simple Lie Algebras -- 1.5 Extensions of Lie Algebras and Co-homology -- 2 Semi-Simple Lie Algebras and Root Systems -- 2.1 Root Space Decomposition -- 2.2 Root Systems -- 2.3 Dynkin Diagram and the Classification of Root Systems -- 2.4 Conjugacy Theorem, Existence and Uniqueness Theorems -- 3 Representation Theory of Lie Algebras -- 3.1 Theorems of Ado and Iwasawa -- 3.2 Cyclic Modules and Weights -- 3.3 Characters and Harish-Chandra's Theorem -- 3.4 Multiplicity Formulas of Weyl, Kostant, and Steinberg -- 4 Chevalley Groups -- 4.1 Classical Linear Groups -- 4.2 Chevalley Basis -- 4.3 Chevalley Groups -- 4.4 Twisted Groups -- 5 Representation Theory of Chevalley Groups -- 5.1 Language of Representation Theory -- 5.2 Representations of Sn, and of GL(2.q) -- 5.3 Steinberg Characters -- 5.4 Principal and Discrete Series Representations -- 5.5 Deligne-Lusztig Generalized Characters -- Appendix Bibliography -- -- Index. |
Altri titoli varianti | Algebra four |
Record Nr. | UNINA-9910484402103321 |
Lal Ramji | ||
Singapore : , : Springer, , [2021] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Algebra and applications . 1 Non-associative algebras and categories / / coordinated by Abdenacer Makhlouf |
Pubbl/distr/stampa | London, England ; ; Hoboken, New Jersey : , : Wiley : , : ISTE, , [2020] |
Descrizione fisica | 1 online resource (369 pages) |
Disciplina | 512.9 |
Soggetto topico | Algebra |
Soggetto genere / forma | Electronic books. |
ISBN |
1-119-81815-X
1-119-81817-6 1-119-81816-8 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Cover -- Half-Title Page -- Title Page -- Copyright Page -- Contents -- Foreword -- 1 Jordan Superalgebras -- 1.1. Introduction -- 1.2. Tits-Kantor-Koecher construction -- 1.3. Basic examples (classical superalgebras) -- 1.4. Brackets -- 1.5. Cheng-Kac superalgebras -- 1.6. Finite dimensional simple Jordan superalgebras -- 1.6.1. Case F is algebraically closed and char F = 0 -- 1.6.2. Case char F = p > -- 2, the even part J¯0 is semisimple -- 1.6.3. Case char F = p > -- 2, the even part J¯0 is not semisimple -- 1.6.4. Non-unital simple Jordan superalgebras -- 1.7. Finite dimensional representations -- 1.7.1. Superalgebras of rank ≥ 3 -- 1.7.2. Superalgebras of rank ≤ 2 -- 1.8. Jordan superconformal algebras -- 1.9. References -- 2 Composition Algebras -- 2.1. Introduction -- 2.2. Quaternions and octonions -- 2.2.1. Quaternions -- 2.2.2. Rotations in three(and four-) dimensional space -- 2.2.3. Octonions -- 2.3. Unital composition algebras -- 2.3.1. The Cayley-Dickson doubling process and the generalized Hurwitz theorem -- 2.3.2. Isotropic Hurwitz algebras -- 2.4. Symmetric composition algebras -- 2.5. Triality -- 2.6. Concluding remarks -- 2.7. Acknowledgments -- 2.8. References -- 3 Graded-Division Algebras -- 3.1. Introduction -- 3.2. Background on gradings -- 3.2.1. Gradings induced by a group homomorphism -- 3.2.2. Weak isomorphism and equivalence -- 3.2.3. Basic properties of division gradings -- 3.2.4. Graded presentations of associative algebras -- 3.2.5. Tensor products of division gradings -- 3.2.6. Loop construction -- 3.2.7. Another construction of graded-simple algebras -- 3.3. Graded-division algebras over algebraically closed fields -- 3.4. Real graded-division associative algebras -- 3.4.1. Simple graded-division algebras -- 3.4.2. Pauli gradings -- 3.4.3. Commutative case.
3.4.4. Non-commutative graded-division algebras with one-dimensional homogeneous components -- 3.4.5. Equivalence classes of graded-division algebras with one-dimensional homogeneous components -- 3.4.6. Graded-division algebras with non-central two-dimensional identity components -- 3.4.7. Graded-division algebras with four-dimensional identity components -- 3.4.8. Classification of real graded-division algebras, up to isomorphism -- 3.5. Real loop algebras with a non-split centroid -- 3.6. Alternative algebras -- 3.6.1. Cayley-Dickson doubling process -- 3.6.2. Gradings on octonion algebras -- 3.6.3. Graded-simple real alternative algebras -- 3.6.4. Graded-division real alternative algebras -- 3.7. Gradings of fields -- 3.8. References -- 4 Non-associative C*-algebras -- 4.1. Introduction -- 4.2. JB-algebras -- 4.3. The non-associative Vidav-Palmer and Gelfand-Naimark theorems -- 4.4. JB*-triples -- 4.5. Past, present and future of non-associative C*-algebras -- 4.6. Acknowledgments -- 4.7. References -- 5 Structure of H -algebras -- 5.1. Introduction -- 5.2. Preliminaries: aspects of the general theory -- 5.3. Ultraproducts of H -algebras -- 5.4. Quadratic H -algebras -- 5.5. Associative H -algebras -- 5.6. Flexible H -algebras -- 5.7. Non-commutative Jordan H -algebras -- 5.8. Jordan H -algebras -- 5.9. Moufang H -algebras -- 5.10. Lie H -algebras -- 5.11. Topics closely related to Lie H -algebras -- 5.12. Two-graded H -algebras -- 5.13. Other topics: beyond the H -algebras -- 5.14. Acknowledgments -- 5.15. References -- 6 Krichever-Novikov Type Algebras: Definitions and Results -- 6.1. Introduction -- 6.2. The Virasoro algebra and its relatives -- 6.3. The geometric picture -- 6.3.1. The geometric realizations of the Witt algebra -- 6.3.2. Arbitrary genus generalizations -- 6.3.3. Meromorphic forms -- 6.4. Algebraic structures. 6.4.1. Associative structure -- 6.4.2. Lie and Poisson algebra structure -- 6.4.3. The vector field algebra and the Lie derivative -- 6.4.4. The algebra of differential operators -- 6.4.5. Differential operators of all degrees -- 6.4.6. Lie superalgebras of half forms -- 6.4.7. Jordan superalgebra -- 6.4.8. Higher genus current algebras -- 6.4.9. KN-type algebras -- 6.5. Almost-graded structure -- 6.5.1. Definition of almost-gradedness -- 6.5.2. Separating cycle and KN pairing -- 6.5.4. The algebras -- 6.5.5. Triangular decomposition and filtrations -- 6.6. Central extensions -- 6.6.1. Central extensions and cocycles -- 6.6.2. Geometric cocycles -- 6.6.3. Uniqueness and classification of central extensions -- 6.7. Examples and generalizations -- 6.7.1. The genus zero and three-point situation -- 6.7.2. Genus zero multipoint algebras - integrable systems -- 6.7.3. Deformations -- 6.8. Lax operator algebras -- 6.9. Fermionic Fock space -- 6.9.1. Semi-infinite forms and fermionic Fock space representations -- 6.9.2. b - c systems -- 6.10. Sugawara representation -- 6.11. Application to moduli space -- 6.12. Acknowledgments -- 6.13. References -- 7 An Introduction to Pre-Lie Algebras -- 7.1. Introduction -- 7.1.1. Explanation of notions -- 7.1.2. Two fundamental properties -- 7.1.3. Some subclasses -- 7.1.4. Organization of this chapter -- 7.2. Some appearances of pre-Lie algebras -- 7.2.2. Deformation complexes of algebras and right-symmetric algebras -- 7.2.3. Rooted tree algebras: free pre-Lie algebras -- 7.2.4. Complex structures on Lie algebras -- 7.2.5. Symplectic structures on Lie groups and Lie algebras, phase spaces of Lie algebras and Kähler structures -- 7.2.6. Vertex algebras -- 7.3. Some basic results and constructions of pre-Lie algebras -- 7.3.1. Some basic results of pre-Lie algebras. 7.3.2. Constructions of pre-Lie algebras from some known structures -- 7.4. Pre-Lie algebras and CYBE -- 7.4.1. The existence of a compatible pre-Lie algebra on a Lie algebra -- 7.4.2. CYBE: unification of tensor and operator forms -- 7.4.3. Pre-Lie algebras, O-operators and CYBE -- 7.4.4. An algebraic interpretation of "left-symmetry": construction from Lie algebras revisited -- 7.5. A larger framework: Lie analogues of Loday algebras -- 7.5.1. Pre-Lie algebras, dendriform algebras and Loday algebras -- 7.5.2. L-dendriform algebras -- 7.5.3. Lie analogues of Loday algebras -- 7.6. References -- 8 Symplectic, Product and Complex Structures on 3-Lie Algebras -- 8.1. Introduction -- 8.2. Preliminaries -- 8.3. Representations of 3-pre-Lie algebras -- 8.4. Symplectic structures and phase spaces of 3-Lie algebras -- 8.5. Product structures on 3-Lie algebras -- 8.6. Complex structures on 3-Lie algebras -- 8.7. Complex product structures on 3-Lie algebras -- 8.8. Para-Kähler structures on 3-Lie algebras -- 8.9. Pseudo-Kähler structures on 3-Lie algebras -- 8.10. References -- 9 Derived Categories -- 9.1. Introduction -- 9.2. Grothendieck's definition -- 9.3. Verdier's definition -- 9.4. Triangulated structure -- 9.5. Derived functors -- 9.6. Derived Morita theory -- 9.7. Dg categories -- 9.7.1. Dg categories and functors -- 9.7.2. The derived category -- 9.7.3. Derived functors -- 9.7.4. Dg quotients -- 9.7.5. Invariants -- 9.8. References -- List of Authors -- Index -- EULA. |
Record Nr. | UNINA-9910555016403321 |
London, England ; ; Hoboken, New Jersey : , : Wiley : , : ISTE, , [2020] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Algebra and applications . 1 Non-associative algebras and categories / / coordinated by Abdenacer Makhlouf |
Pubbl/distr/stampa | London, England ; ; Hoboken, New Jersey : , : Wiley : , : ISTE, , [2020] |
Descrizione fisica | 1 online resource (369 pages) |
Disciplina | 512.9 |
Soggetto topico | Algebra |
ISBN |
1-119-81815-X
1-119-81817-6 1-119-81816-8 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Cover -- Half-Title Page -- Title Page -- Copyright Page -- Contents -- Foreword -- 1 Jordan Superalgebras -- 1.1. Introduction -- 1.2. Tits-Kantor-Koecher construction -- 1.3. Basic examples (classical superalgebras) -- 1.4. Brackets -- 1.5. Cheng-Kac superalgebras -- 1.6. Finite dimensional simple Jordan superalgebras -- 1.6.1. Case F is algebraically closed and char F = 0 -- 1.6.2. Case char F = p > -- 2, the even part J¯0 is semisimple -- 1.6.3. Case char F = p > -- 2, the even part J¯0 is not semisimple -- 1.6.4. Non-unital simple Jordan superalgebras -- 1.7. Finite dimensional representations -- 1.7.1. Superalgebras of rank ≥ 3 -- 1.7.2. Superalgebras of rank ≤ 2 -- 1.8. Jordan superconformal algebras -- 1.9. References -- 2 Composition Algebras -- 2.1. Introduction -- 2.2. Quaternions and octonions -- 2.2.1. Quaternions -- 2.2.2. Rotations in three(and four-) dimensional space -- 2.2.3. Octonions -- 2.3. Unital composition algebras -- 2.3.1. The Cayley-Dickson doubling process and the generalized Hurwitz theorem -- 2.3.2. Isotropic Hurwitz algebras -- 2.4. Symmetric composition algebras -- 2.5. Triality -- 2.6. Concluding remarks -- 2.7. Acknowledgments -- 2.8. References -- 3 Graded-Division Algebras -- 3.1. Introduction -- 3.2. Background on gradings -- 3.2.1. Gradings induced by a group homomorphism -- 3.2.2. Weak isomorphism and equivalence -- 3.2.3. Basic properties of division gradings -- 3.2.4. Graded presentations of associative algebras -- 3.2.5. Tensor products of division gradings -- 3.2.6. Loop construction -- 3.2.7. Another construction of graded-simple algebras -- 3.3. Graded-division algebras over algebraically closed fields -- 3.4. Real graded-division associative algebras -- 3.4.1. Simple graded-division algebras -- 3.4.2. Pauli gradings -- 3.4.3. Commutative case.
3.4.4. Non-commutative graded-division algebras with one-dimensional homogeneous components -- 3.4.5. Equivalence classes of graded-division algebras with one-dimensional homogeneous components -- 3.4.6. Graded-division algebras with non-central two-dimensional identity components -- 3.4.7. Graded-division algebras with four-dimensional identity components -- 3.4.8. Classification of real graded-division algebras, up to isomorphism -- 3.5. Real loop algebras with a non-split centroid -- 3.6. Alternative algebras -- 3.6.1. Cayley-Dickson doubling process -- 3.6.2. Gradings on octonion algebras -- 3.6.3. Graded-simple real alternative algebras -- 3.6.4. Graded-division real alternative algebras -- 3.7. Gradings of fields -- 3.8. References -- 4 Non-associative C*-algebras -- 4.1. Introduction -- 4.2. JB-algebras -- 4.3. The non-associative Vidav-Palmer and Gelfand-Naimark theorems -- 4.4. JB*-triples -- 4.5. Past, present and future of non-associative C*-algebras -- 4.6. Acknowledgments -- 4.7. References -- 5 Structure of H -algebras -- 5.1. Introduction -- 5.2. Preliminaries: aspects of the general theory -- 5.3. Ultraproducts of H -algebras -- 5.4. Quadratic H -algebras -- 5.5. Associative H -algebras -- 5.6. Flexible H -algebras -- 5.7. Non-commutative Jordan H -algebras -- 5.8. Jordan H -algebras -- 5.9. Moufang H -algebras -- 5.10. Lie H -algebras -- 5.11. Topics closely related to Lie H -algebras -- 5.12. Two-graded H -algebras -- 5.13. Other topics: beyond the H -algebras -- 5.14. Acknowledgments -- 5.15. References -- 6 Krichever-Novikov Type Algebras: Definitions and Results -- 6.1. Introduction -- 6.2. The Virasoro algebra and its relatives -- 6.3. The geometric picture -- 6.3.1. The geometric realizations of the Witt algebra -- 6.3.2. Arbitrary genus generalizations -- 6.3.3. Meromorphic forms -- 6.4. Algebraic structures. 6.4.1. Associative structure -- 6.4.2. Lie and Poisson algebra structure -- 6.4.3. The vector field algebra and the Lie derivative -- 6.4.4. The algebra of differential operators -- 6.4.5. Differential operators of all degrees -- 6.4.6. Lie superalgebras of half forms -- 6.4.7. Jordan superalgebra -- 6.4.8. Higher genus current algebras -- 6.4.9. KN-type algebras -- 6.5. Almost-graded structure -- 6.5.1. Definition of almost-gradedness -- 6.5.2. Separating cycle and KN pairing -- 6.5.4. The algebras -- 6.5.5. Triangular decomposition and filtrations -- 6.6. Central extensions -- 6.6.1. Central extensions and cocycles -- 6.6.2. Geometric cocycles -- 6.6.3. Uniqueness and classification of central extensions -- 6.7. Examples and generalizations -- 6.7.1. The genus zero and three-point situation -- 6.7.2. Genus zero multipoint algebras - integrable systems -- 6.7.3. Deformations -- 6.8. Lax operator algebras -- 6.9. Fermionic Fock space -- 6.9.1. Semi-infinite forms and fermionic Fock space representations -- 6.9.2. b - c systems -- 6.10. Sugawara representation -- 6.11. Application to moduli space -- 6.12. Acknowledgments -- 6.13. References -- 7 An Introduction to Pre-Lie Algebras -- 7.1. Introduction -- 7.1.1. Explanation of notions -- 7.1.2. Two fundamental properties -- 7.1.3. Some subclasses -- 7.1.4. Organization of this chapter -- 7.2. Some appearances of pre-Lie algebras -- 7.2.2. Deformation complexes of algebras and right-symmetric algebras -- 7.2.3. Rooted tree algebras: free pre-Lie algebras -- 7.2.4. Complex structures on Lie algebras -- 7.2.5. Symplectic structures on Lie groups and Lie algebras, phase spaces of Lie algebras and Kähler structures -- 7.2.6. Vertex algebras -- 7.3. Some basic results and constructions of pre-Lie algebras -- 7.3.1. Some basic results of pre-Lie algebras. 7.3.2. Constructions of pre-Lie algebras from some known structures -- 7.4. Pre-Lie algebras and CYBE -- 7.4.1. The existence of a compatible pre-Lie algebra on a Lie algebra -- 7.4.2. CYBE: unification of tensor and operator forms -- 7.4.3. Pre-Lie algebras, O-operators and CYBE -- 7.4.4. An algebraic interpretation of "left-symmetry": construction from Lie algebras revisited -- 7.5. A larger framework: Lie analogues of Loday algebras -- 7.5.1. Pre-Lie algebras, dendriform algebras and Loday algebras -- 7.5.2. L-dendriform algebras -- 7.5.3. Lie analogues of Loday algebras -- 7.6. References -- 8 Symplectic, Product and Complex Structures on 3-Lie Algebras -- 8.1. Introduction -- 8.2. Preliminaries -- 8.3. Representations of 3-pre-Lie algebras -- 8.4. Symplectic structures and phase spaces of 3-Lie algebras -- 8.5. Product structures on 3-Lie algebras -- 8.6. Complex structures on 3-Lie algebras -- 8.7. Complex product structures on 3-Lie algebras -- 8.8. Para-Kähler structures on 3-Lie algebras -- 8.9. Pseudo-Kähler structures on 3-Lie algebras -- 8.10. References -- 9 Derived Categories -- 9.1. Introduction -- 9.2. Grothendieck's definition -- 9.3. Verdier's definition -- 9.4. Triangulated structure -- 9.5. Derived functors -- 9.6. Derived Morita theory -- 9.7. Dg categories -- 9.7.1. Dg categories and functors -- 9.7.2. The derived category -- 9.7.3. Derived functors -- 9.7.4. Dg quotients -- 9.7.5. Invariants -- 9.8. References -- List of Authors -- Index -- EULA. |
Record Nr. | UNINA-9910677261803321 |
London, England ; ; Hoboken, New Jersey : , : Wiley : , : ISTE, , [2020] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Algebra and applications . 1 Non-associative algebras and categories / / coordinated by Abdenacer Makhlouf |
Pubbl/distr/stampa | London, England ; ; Hoboken, New Jersey : , : Wiley : , : ISTE, , [2020] |
Descrizione fisica | 1 online resource (369 pages) |
Disciplina | 512.9 |
Soggetto topico | Algebra |
ISBN |
1-119-81815-X
1-119-81817-6 1-119-81816-8 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Cover -- Half-Title Page -- Title Page -- Copyright Page -- Contents -- Foreword -- 1 Jordan Superalgebras -- 1.1. Introduction -- 1.2. Tits-Kantor-Koecher construction -- 1.3. Basic examples (classical superalgebras) -- 1.4. Brackets -- 1.5. Cheng-Kac superalgebras -- 1.6. Finite dimensional simple Jordan superalgebras -- 1.6.1. Case F is algebraically closed and char F = 0 -- 1.6.2. Case char F = p > -- 2, the even part J¯0 is semisimple -- 1.6.3. Case char F = p > -- 2, the even part J¯0 is not semisimple -- 1.6.4. Non-unital simple Jordan superalgebras -- 1.7. Finite dimensional representations -- 1.7.1. Superalgebras of rank ≥ 3 -- 1.7.2. Superalgebras of rank ≤ 2 -- 1.8. Jordan superconformal algebras -- 1.9. References -- 2 Composition Algebras -- 2.1. Introduction -- 2.2. Quaternions and octonions -- 2.2.1. Quaternions -- 2.2.2. Rotations in three(and four-) dimensional space -- 2.2.3. Octonions -- 2.3. Unital composition algebras -- 2.3.1. The Cayley-Dickson doubling process and the generalized Hurwitz theorem -- 2.3.2. Isotropic Hurwitz algebras -- 2.4. Symmetric composition algebras -- 2.5. Triality -- 2.6. Concluding remarks -- 2.7. Acknowledgments -- 2.8. References -- 3 Graded-Division Algebras -- 3.1. Introduction -- 3.2. Background on gradings -- 3.2.1. Gradings induced by a group homomorphism -- 3.2.2. Weak isomorphism and equivalence -- 3.2.3. Basic properties of division gradings -- 3.2.4. Graded presentations of associative algebras -- 3.2.5. Tensor products of division gradings -- 3.2.6. Loop construction -- 3.2.7. Another construction of graded-simple algebras -- 3.3. Graded-division algebras over algebraically closed fields -- 3.4. Real graded-division associative algebras -- 3.4.1. Simple graded-division algebras -- 3.4.2. Pauli gradings -- 3.4.3. Commutative case.
3.4.4. Non-commutative graded-division algebras with one-dimensional homogeneous components -- 3.4.5. Equivalence classes of graded-division algebras with one-dimensional homogeneous components -- 3.4.6. Graded-division algebras with non-central two-dimensional identity components -- 3.4.7. Graded-division algebras with four-dimensional identity components -- 3.4.8. Classification of real graded-division algebras, up to isomorphism -- 3.5. Real loop algebras with a non-split centroid -- 3.6. Alternative algebras -- 3.6.1. Cayley-Dickson doubling process -- 3.6.2. Gradings on octonion algebras -- 3.6.3. Graded-simple real alternative algebras -- 3.6.4. Graded-division real alternative algebras -- 3.7. Gradings of fields -- 3.8. References -- 4 Non-associative C*-algebras -- 4.1. Introduction -- 4.2. JB-algebras -- 4.3. The non-associative Vidav-Palmer and Gelfand-Naimark theorems -- 4.4. JB*-triples -- 4.5. Past, present and future of non-associative C*-algebras -- 4.6. Acknowledgments -- 4.7. References -- 5 Structure of H -algebras -- 5.1. Introduction -- 5.2. Preliminaries: aspects of the general theory -- 5.3. Ultraproducts of H -algebras -- 5.4. Quadratic H -algebras -- 5.5. Associative H -algebras -- 5.6. Flexible H -algebras -- 5.7. Non-commutative Jordan H -algebras -- 5.8. Jordan H -algebras -- 5.9. Moufang H -algebras -- 5.10. Lie H -algebras -- 5.11. Topics closely related to Lie H -algebras -- 5.12. Two-graded H -algebras -- 5.13. Other topics: beyond the H -algebras -- 5.14. Acknowledgments -- 5.15. References -- 6 Krichever-Novikov Type Algebras: Definitions and Results -- 6.1. Introduction -- 6.2. The Virasoro algebra and its relatives -- 6.3. The geometric picture -- 6.3.1. The geometric realizations of the Witt algebra -- 6.3.2. Arbitrary genus generalizations -- 6.3.3. Meromorphic forms -- 6.4. Algebraic structures. 6.4.1. Associative structure -- 6.4.2. Lie and Poisson algebra structure -- 6.4.3. The vector field algebra and the Lie derivative -- 6.4.4. The algebra of differential operators -- 6.4.5. Differential operators of all degrees -- 6.4.6. Lie superalgebras of half forms -- 6.4.7. Jordan superalgebra -- 6.4.8. Higher genus current algebras -- 6.4.9. KN-type algebras -- 6.5. Almost-graded structure -- 6.5.1. Definition of almost-gradedness -- 6.5.2. Separating cycle and KN pairing -- 6.5.4. The algebras -- 6.5.5. Triangular decomposition and filtrations -- 6.6. Central extensions -- 6.6.1. Central extensions and cocycles -- 6.6.2. Geometric cocycles -- 6.6.3. Uniqueness and classification of central extensions -- 6.7. Examples and generalizations -- 6.7.1. The genus zero and three-point situation -- 6.7.2. Genus zero multipoint algebras - integrable systems -- 6.7.3. Deformations -- 6.8. Lax operator algebras -- 6.9. Fermionic Fock space -- 6.9.1. Semi-infinite forms and fermionic Fock space representations -- 6.9.2. b - c systems -- 6.10. Sugawara representation -- 6.11. Application to moduli space -- 6.12. Acknowledgments -- 6.13. References -- 7 An Introduction to Pre-Lie Algebras -- 7.1. Introduction -- 7.1.1. Explanation of notions -- 7.1.2. Two fundamental properties -- 7.1.3. Some subclasses -- 7.1.4. Organization of this chapter -- 7.2. Some appearances of pre-Lie algebras -- 7.2.2. Deformation complexes of algebras and right-symmetric algebras -- 7.2.3. Rooted tree algebras: free pre-Lie algebras -- 7.2.4. Complex structures on Lie algebras -- 7.2.5. Symplectic structures on Lie groups and Lie algebras, phase spaces of Lie algebras and Kähler structures -- 7.2.6. Vertex algebras -- 7.3. Some basic results and constructions of pre-Lie algebras -- 7.3.1. Some basic results of pre-Lie algebras. 7.3.2. Constructions of pre-Lie algebras from some known structures -- 7.4. Pre-Lie algebras and CYBE -- 7.4.1. The existence of a compatible pre-Lie algebra on a Lie algebra -- 7.4.2. CYBE: unification of tensor and operator forms -- 7.4.3. Pre-Lie algebras, O-operators and CYBE -- 7.4.4. An algebraic interpretation of "left-symmetry": construction from Lie algebras revisited -- 7.5. A larger framework: Lie analogues of Loday algebras -- 7.5.1. Pre-Lie algebras, dendriform algebras and Loday algebras -- 7.5.2. L-dendriform algebras -- 7.5.3. Lie analogues of Loday algebras -- 7.6. References -- 8 Symplectic, Product and Complex Structures on 3-Lie Algebras -- 8.1. Introduction -- 8.2. Preliminaries -- 8.3. Representations of 3-pre-Lie algebras -- 8.4. Symplectic structures and phase spaces of 3-Lie algebras -- 8.5. Product structures on 3-Lie algebras -- 8.6. Complex structures on 3-Lie algebras -- 8.7. Complex product structures on 3-Lie algebras -- 8.8. Para-Kähler structures on 3-Lie algebras -- 8.9. Pseudo-Kähler structures on 3-Lie algebras -- 8.10. References -- 9 Derived Categories -- 9.1. Introduction -- 9.2. Grothendieck's definition -- 9.3. Verdier's definition -- 9.4. Triangulated structure -- 9.5. Derived functors -- 9.6. Derived Morita theory -- 9.7. Dg categories -- 9.7.1. Dg categories and functors -- 9.7.2. The derived category -- 9.7.3. Derived functors -- 9.7.4. Dg quotients -- 9.7.5. Invariants -- 9.8. References -- List of Authors -- Index -- EULA. |
Record Nr. | UNINA-9910820822103321 |
London, England ; ; Hoboken, New Jersey : , : Wiley : , : ISTE, , [2020] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Algebra and number theory : a selection of highlights / / Benjamin Fine [and four others] |
Autore | Fine Benjamin |
Pubbl/distr/stampa | Berlin, [Germany] ; ; Boston, [Massachusetts] : , : De Gruyter, , 2017 |
Descrizione fisica | 1 online resource (332 pages) : illustrations |
Disciplina | 512.9 |
Collana | De Gruyter Textbook |
Soggetto topico |
Algebra
Number theory |
Soggetto genere / forma | Electronic books. |
ISBN |
3-11-051626-8
3-11-051614-4 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Frontmatter -- Preface -- Contents -- 1. The natural, integral and rational numbers -- 2. Division and factorization in the integers -- 3. Modular arithmetic -- 4. Exceptional numbers -- 5. Pythagorean triples and sums of squares -- 6. Polynomials and unique factorization -- 7. Field extensions and splitting fields -- 8. Permutations and symmetric polynomials -- 9. Real numbers -- 10. The complex numbers, the Fundamental Theorem of Algebra and polynomial equations -- 11. Quadratic number fields and Pell's equation -- 12. Transcendental numbers and the numbers e and π -- 13. Compass and straightedge constructions and the classical problems -- 14. Euclidean vector spaces -- Bibliography -- Index |
Record Nr. | UNINA-9910467837503321 |
Fine Benjamin | ||
Berlin, [Germany] ; ; Boston, [Massachusetts] : , : De Gruyter, , 2017 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Algebra and number theory : a selection of highlights / / Benjamin Fine [and four others] |
Autore | Fine Benjamin |
Pubbl/distr/stampa | Berlin, [Germany] ; ; Boston, [Massachusetts] : , : De Gruyter, , 2017 |
Descrizione fisica | 1 online resource (332 pages) : illustrations |
Disciplina | 512.9 |
Collana | De Gruyter Textbook |
Soggetto topico |
Algebra
Number theory |
ISBN |
3-11-051626-8
3-11-051614-4 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Frontmatter -- Preface -- Contents -- 1. The natural, integral and rational numbers -- 2. Division and factorization in the integers -- 3. Modular arithmetic -- 4. Exceptional numbers -- 5. Pythagorean triples and sums of squares -- 6. Polynomials and unique factorization -- 7. Field extensions and splitting fields -- 8. Permutations and symmetric polynomials -- 9. Real numbers -- 10. The complex numbers, the Fundamental Theorem of Algebra and polynomial equations -- 11. Quadratic number fields and Pell's equation -- 12. Transcendental numbers and the numbers e and π -- 13. Compass and straightedge constructions and the classical problems -- 14. Euclidean vector spaces -- Bibliography -- Index |
Record Nr. | UNINA-9910795045003321 |
Fine Benjamin | ||
Berlin, [Germany] ; ; Boston, [Massachusetts] : , : De Gruyter, , 2017 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|