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Algebra & number theory
| Algebra & number theory |
| Pubbl/distr/stampa | Berkeley, CA, : Mathematical Sciences Publishers, [2007]- |
| Disciplina | 550 |
| Soggetto topico |
Algebra
Number theory Algèbre Nombres, Théorie des |
| Soggetto genere / forma | Periodicals. |
| ISSN | 1944-7833 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Periodico |
| Lingua di pubblicazione | eng |
| Altri titoli varianti |
Algebra and number theory
ANT |
| Record Nr. | UNINA-9910146927103321 |
| Berkeley, CA, : Mathematical Sciences Publishers, [2007]- | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Algebra 1 [[electronic resource] ] : Groups, Rings, Fields and Arithmetic / / by Ramji Lal
| Algebra 1 [[electronic resource] ] : Groups, Rings, Fields and Arithmetic / / by Ramji Lal |
| Autore | Lal Ramji |
| Edizione | [1st ed. 2017.] |
| Pubbl/distr/stampa | Singapore : , : Springer Singapore : , : Imprint : Springer, , 2017 |
| Descrizione fisica | 1 online resource (XVII, 433 p.) |
| Disciplina | 512.2 |
| Collana | Infosys Science Foundation Series in Mathematical Sciences |
| Soggetto topico |
Group theory
Associative rings Rings (Algebra) Nonassociative rings Commutative algebra Commutative rings Algebra Field theory (Physics) Number theory Group Theory and Generalizations Associative Rings and Algebras Non-associative Rings and Algebras Commutative Rings and Algebras Field Theory and Polynomials Number Theory |
| ISBN | 981-10-4253-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Chapter 1. Language of mathematics 1 (Logic) -- Chapter 2. Language Of Mathematics 2 (Set Theory) -- Chapter 3. Number System -- Chapter 4. Group Theory -- Chapter 5. Fundamental Theorems -- Chapter 6. Permutation groups and Classical Groups -- Chapter 7. Elementary Theory of Rings and Fields -- Chapter 8. Number Theory 2 -- Chapter 9. Structure theory of groups -- Chapter 10. Structure theory continued -- Chapter 11. Arithmetic in Rings. |
| Record Nr. | UNINA-9910254275103321 |
Lal Ramji
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| Singapore : , : Springer Singapore : , : Imprint : Springer, , 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Algebra 2 [[electronic resource] ] : Linear Algebra, Galois Theory, Representation theory, Group extensions and Schur Multiplier / / by Ramji Lal
| 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 |
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Lal Ramji
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| Singapore : , : Springer Singapore : , : Imprint : Springer, , 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Algebra 2 / B. L. van der Waerden ; unter benutzung von Vorlesungen von E. Artin und E. Noether
| Algebra 2 / B. L. van der Waerden ; unter benutzung von Vorlesungen von E. Artin und E. Noether |
| Autore | Waerden, Bartel Laeendert : van der |
| Pubbl/distr/stampa | Berlin... [etc.] : Springer, 1967 |
| Descrizione fisica | X, 300 p. ; 21 cm. |
| Disciplina | 512 |
| Soggetto topico | Algebra |
| ISBN | 3-540-03869-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | ger |
| Record Nr. | UNIBAS-000005244 |
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Waerden, Bartel Laeendert : van der
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| Berlin... [etc.] : Springer, 1967 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. della Basilicata | ||
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Algebra 4 : lie algebras, Chevalley groups, and their representations / / Ramji Lal
| 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 |
| 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 |
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Lal Ramji
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| Singapore : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Algebra 4 : lie algebras, Chevalley groups, and their representations / / Ramji Lal
| 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 |
| 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 |
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Lal Ramji
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| Singapore : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Algebra ad uso delle scuole medie inferiori / Tommaso Cifarelli
| Algebra ad uso delle scuole medie inferiori / Tommaso Cifarelli |
| Autore | Cifarelli, Tommaso |
| Pubbl/distr/stampa | Napoli : Morano, [19..] |
| Descrizione fisica | v. ; 19 cm |
| Disciplina | 512 |
| Soggetto topico | Algebra |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | ita |
| Record Nr. | UNISALENTO-b13108827 |
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Cifarelli, Tommaso
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| Napoli : Morano, [19..] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Algebra and applications . 1 Non-associative algebras and categories / / coordinated by Abdenacer Makhlouf
| 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 | ||
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Algebra and applications 2 : combinatorial algebra and Hopf algebras / / edited by Abdenacer Makhlouf
| Algebra and applications 2 : combinatorial algebra and Hopf algebras / / edited by Abdenacer Makhlouf |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : John Wiley & Sons, Incorporated, , [2021] |
| Descrizione fisica | 1 online resource (336 pages) |
| Disciplina | 512 |
| Soggetto topico | Algebra |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-119-88090-4
1-119-88091-2 1-119-88089-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Half-Title Page -- Title Page -- Copyright Page -- Contents -- Preface -- 1. Algebraic Background for Numerical Methods, Control Theory and Renormalization -- 1.1. Introduction -- 1.2. Hopf algebras: general properties -- 1.2.1. Algebras -- 1.2.2. Coalgebras -- 1.2.3. Convolution product -- 1.2.4. Bialgebras and Hopf algebras -- 1.2.5. Some simple examples of Hopf algebras -- 1.2.6. Some basic properties of Hopf algebras -- 1.3. Connected Hopf algebras -- 1.3.1. Connected graded bialgebras -- 1.3.2. An example: the Hopf algebra of decorated rooted trees -- 1.3.3. Connected filtered bialgebras -- 1.3.4. The convolution product -- 1.3.5. Characters -- 1.3.6. Group schemes and the Cartier-Milnor-Moore-Quillen theorem -- 1.3.7. Renormalization in connected filtered Hopf algebras -- 1.4. Pre-Lie algebras -- 1.4.1. Definition and general properties -- 1.4.2. The group of formal flows -- 1.4.3. The pre-Lie Poincaré-Birkhoff-Witt theorem -- 1.5. Algebraic operads -- 1.5.1. Manipulating algebraic operations -- 1.5.2. The operad of multi-linear operations -- 1.5.3. A definition for linear operads -- 1.5.4. A few examples of operads -- 1.6. Pre-Lie algebras (continued) -- 1.6.1. Pre-Lie algebras and augmented operads -- 1.6.2. A pedestrian approach to free pre-Lie algebra -- 1.6.3. Right-sided commutative Hopf algebras and the Loday-Ronco theorem -- 1.6.4. Pre-Lie algebras of vector fields -- 1.6.5. B-series, composition and substitution -- 1.7. Other related algebraic structures -- 1.7.1. NAP algebras -- 1.7.2. Novikov algebras -- 1.7.3. Assosymmetric algebras -- 1.7.4. Dendriform algebras -- 1.7.5. Post-Lie algebras -- 1.8. References -- 2. From Iterated Integrals and Chronological Calculus to Hopf and Rota-Baxter Algebras -- 2.1. Introduction -- 2.2. Generalized iterated integrals -- 2.2.1. Permutations and simplices.
2.2.2. Descents, NCSF and the BCH formula -- 2.2.3. Rooted trees and nonlinear differential equations -- 2.2.4. Flows and Hopf algebraic structures -- 2.3. Advances in chronological calculus -- 2.3.1. Chronological calculus and half-shuffles -- 2.3.2. Chronological calculus and pre-Lie products -- 2.3.3. Time-ordered products and enveloping algebras -- 2.3.4. Formal flows and Hopf algebraic structures -- 2.4. Rota-Baxter algebras -- 2.4.1. Origin -- 2.4.2. Definition and examples -- 2.4.3. Related algebraic structures -- 2.4.4. Atkinson's factorization and Bogoliubov's recursion -- 2.4.5. Spitzer's identity: commutative case -- 2.4.6. Free commutative Rota-Baxter algebras -- 2.4.7. Spitzer's identity: noncommutative case -- 2.4.8. Free Rota-Baxter algebras -- 2.5. References -- 3. Noncommutative Symmetric Functions, Lie Series and Descent Algebras -- 3.1. Introduction -- 3.2. Classical symmetric functions -- 3.2.1. Symmetric polynomials -- 3.2.2. The Hopf algebra of symmetric functions -- 3.2.3. The λ-ring notation -- 3.2.4. Symmetric functions and formal power series -- 3.2.5. Duality -- 3.3. Noncommutative symmetric functions -- 3.3.1. Basic definitions -- 3.3.2. Generators and linear bases -- 3.3.3. Duality -- 3.3.4. Solomon's descent algebras -- 3.4. Lie series and Lie idempotents -- 3.4.1. Permutational operators on tensor spaces -- 3.4.2. The Hausdorff series -- 3.4.3. Lie idempotents in the descent algebra -- 3.5. Lie idempotents as noncommutative symmetric functions -- 3.5.1. Noncommutative power-sums -- 3.5.2. The Magnus expansion -- 3.5.3. The continuous BCH expansion -- 3.5.4. Another proof of the Magnus expansion -- 3.5.5. The (1 - q) -transform -- 3.5.6. Hopf algebras enter the scene -- 3.5.7. A one-parameter family of Lie idempotents -- 3.5.8. The iterated q-bracketing and its diagonalization. 3.6. Decompositions of the descent algebras -- 3.6.1. Complete families of minimal orthogonal idempotents -- 3.6.2. Eulerian idempotents -- 3.6.3. Generalized Eulerian idempotents -- 3.7. Decompositions of the tensor algebra -- 3.8. General deformations -- 3.9. Lie quasi-idempotents as Lie polynomials -- 3.9.1. The left derivative -- 3.9.2. Multilinear Lie polynomials -- 3.9.3. Decompositions on other bases -- 3.10. Permutations and free quasi-symmetric functions -- 3.10.1. Free quasi-symmetric functions -- 3.11. Packed words and word quasi-symmetric functions -- 3.12. References -- 4. From Runge-Kutta Methods to Hopf Algebras of Rooted Trees -- 4.1. Numerical integration methods for ordinary differential equations -- 4.1.1. Introduction -- 4.1.2. Runge-Kutta methods -- 4.2. Algebraic theory of Runge-Kutta methods -- 4.2.1. The order conditions of RK methods -- 4.2.2. The independence of order conditions -- 4.2.3. Proof of necessary and sufficient order conditions -- 4.2.4. Composition of RK methods, rooted trees and forests -- 4.2.5. The Butcher group -- 4.2.6. Equivalence classes of RK methods -- 4.2.7. Bibliographical comments -- 4.3. B-series and related formal expansions -- 4.3.1. B-series -- 4.3.2. Backward error analysis, the exponential and the logarithm -- 4.3.3. Series of linear differential operators -- 4.3.4. The Lie algebra of the Butcher group -- 4.3.5. The pre-Lie algebra structure on ɡ -- 4.3.6. Bibliographical comments -- 4.4. Hopf algebras of rooted trees -- 4.4.1. The commutative Hopf algebra of rooted trees -- 4.4.2. The dual algebra Н* and the dual Hopf algebra H° -- 4.4.3. B-series and series of differential operators revisited -- 4.4.4. A universal property of the commutative Hopf algebra of rooted trees -- 4.4.5. The substitution law -- 4.4.6. Bibliographical comments -- 4.5. References. 5. Combinatorial Algebra in Controllability and Optimal Control -- 5.1. Introduction -- 5.1.1. Motivation: idealized examples -- 5.1.2. Controlled dynamical systems -- 5.1.3. Fundamental questions in control -- 5.2. Analytic foundations -- 5.2.1. State-space models and vector fields on manifolds -- 5.2.2. Chronological calculus -- 5.2.3. Piecewise constant controls and the Baker-Campbell-Hausdorff formula -- 5.2.4. Picard iteration and formal series solutions -- 5.2.5. The Chen-Fliess series and abstractions -- 5.3. Controllability and optimality -- 5.3.1. Reachable sets and accessibility -- 5.3.2. Small-time local controllability -- 5.3.3. Nilpotent approximating systems -- 5.3.4. Optimality and the maximum principle -- 5.3.5. Control variations and approximating cones -- 5.4. Product expansions and realizations -- 5.4.1. Variation of parameters and exponential products -- 5.4.2. Computations using Zinbiel products -- 5.4.3. Exponential products and normal forms for nilpotent systems -- 5.4.4. Logarithm of the Chen series -- 5.5. References -- 6. Algebra is Geometry is Algebra - Interactions Between Hopf Algebras, Infinite Dimensional Geometry and Application -- 6.1. The Butcher group and the Connes-Kreimer algebra -- 6.1.1. The Butcher group and B-series from numerical analysis -- 6.1.2. Beyond the Butcher group -- 6.2. Character groups of graded and connected Hopf algebras -- 6.2.1. The exponential and logarithm -- 6.3. Controlled groups of characters -- 6.3.1. Conventions for this section -- 6.3.2. Combinatorial Hopf algebras and the inverse factorial character -- 6.4. Appendix: Calculus in locally convex spaces -- 6.4.1. Cr -Manifolds and Cr -mappings between them -- 6.5. References -- List of Authors -- Index -- EULA. |
| Record Nr. | UNINA-9910555013003321 |
| Hoboken, New Jersey : , : John Wiley & Sons, Incorporated, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Algebra and Coalgebra in Computer Science : 4th International Conference, CALCO 2011, Winchester, UK, August 30 - September 2, 2011, Proceedings / / edited by Andrea Corradini, Bartek Klin, Corina Cîrstea
| Algebra and Coalgebra in Computer Science : 4th International Conference, CALCO 2011, Winchester, UK, August 30 - September 2, 2011, Proceedings / / edited by Andrea Corradini, Bartek Klin, Corina Cîrstea |
| Edizione | [1st edition] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer, , [2011] |
| Descrizione fisica | 1 online resource (XI, 420 pages) : 118 illustrations., 6 illustrations in color |
| Disciplina | 004.0151 |
| Collana | Theoretical computer science and general issues |
| Soggetto topico |
Computer science - Mathematics
Algebra |
| ISBN | 3-642-22944-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996466054703316 |
| Berlin, Heidelberg : , : Springer, , [2011] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Soggetto topico
-
Algebra
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