Info
- Utilizzare la checkbox di selezione a fianco di ciascun documento per attivare le funzionalità di stampa, invio email, download nei formati disponibili del (i) record.
Groups, rings, and group rings : International Conference : Groups, Rings, and Group Rings, July 28-August 2, 2008, Ubatuba, Brazil / / Antonio Giambruno, César Polcino Milies, Sudarshan K. Sehgal, editors
| Groups, rings, and group rings : International Conference : Groups, Rings, and Group Rings, July 28-August 2, 2008, Ubatuba, Brazil / / Antonio Giambruno, César Polcino Milies, Sudarshan K. Sehgal, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2009] |
| Descrizione fisica | 1 online resource (282 p.) |
| Disciplina | 512/.2 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Group theory
Group rings Rings (Algebra) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
0-8218-8178-7
0-8218-4771-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""The radical of the four generated algebra of alternating type""; ""Globalization of partial actions on semiprime rings""; ""The Colombeau quaternion algebra""; ""Parabolic subgroups of real direct limit Lie groups""; ""Parabolic sets of roots""; ""Some results on *-minimal algebras with involution""; ""Invariants of partial group algebras of finite p-groups""; ""Units of ZCp""; ""Algebraic Elements as Free Factors in Simple Artinian Rings""; ""Special units, unipotent units and free groups in group algebras""
""Explicit realizations of simple weight modules of classical Lie superalgebras""""Combinatorial aspects in the computation of proper multiplicities""; ""An estimate of the dimension of the varieties of alternative and Jordan algebras""; ""On growth of almost polynilpotent Lie algebras""; ""Graded identities for Lie algebras""; ""Polynomial codimension growth of graded algebras""; ""Euclidean Bianchi groups are conjugacy separable""; ""Comparability, distributivity and non-commutative Ï?-rings""; ""Algebras having bases consisting entirely of units"" ""On the growth of varieties of algebras""""0-Dialgebras with bar-unity, Rota-Baxter and 3-Leibniz algebras""; ""The Golod-Shafarevich counterexample without Hilbert series""; ""Automorphism groups of semi-homogeneous trees"" |
| Record Nr. | UNINA-9910479998003321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2009] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Groups, rings, and group rings : International Conference : Groups, Rings, and Group Rings, July 28-August 2, 2008, Ubatuba, Brazil / / Antonio Giambruno, César Polcino Milies, Sudarshan K. Sehgal, editors
| Groups, rings, and group rings : International Conference : Groups, Rings, and Group Rings, July 28-August 2, 2008, Ubatuba, Brazil / / Antonio Giambruno, César Polcino Milies, Sudarshan K. Sehgal, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2009] |
| Descrizione fisica | 1 online resource (282 p.) |
| Disciplina | 512/.2 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Group theory
Group rings Rings (Algebra) |
| ISBN |
0-8218-8178-7
0-8218-4771-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Contents -- Preface -- The radical of the four generated algebra of alternating type -- Globalization of partial actions on semiprime rings -- The Colombeau quaternion algebra -- Parabolic subgroups of real direct limit Lie groups -- Parabolic sets of roots -- Some results on *-minimal algebras with involution -- Invariants of partial group algebras of finite p-groups -- Units of ZCp -- Algebraic Elements as Free Factors in Simple Artinian Rings -- Special units, unipotent units and free groups in group algebras -- Explicit realizations of simple weight modules of classical Lie superalgebras -- Combinatorial aspects in the computation of proper multiplicities -- An estimate of the dimension of the varieties of alternative and Jordan algebras -- On growth of almost polynilpotent Lie algebras -- Graded identities for Lie algebras -- Polynomial codimension growth of graded algebras -- Euclidean Bianchi groups are conjugacy separable -- Comparability, distributivity and non-commutative Ï?-rings -- Algebras having bases consisting entirely of units -- On the growth of varieties of algebras -- 0-Dialgebras with bar-unity, Rota-Baxter and 3-Leibniz algebras -- The Golod-Shafarevich counterexample without Hilbert series -- Automorphism groups of semi-homogeneous trees. |
| Altri titoli varianti | International Conference : Groups, Rings, and Group Rings, July 28-August 2, 2008, Ubatuba, Brazil |
| Record Nr. | UNINA-9910788797703321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2009] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Groups, rings, and group rings : International Conference : Groups, Rings, and Group Rings, July 28-August 2, 2008, Ubatuba, Brazil / / Antonio Giambruno, César Polcino Milies, Sudarshan K. Sehgal, editors
| Groups, rings, and group rings : International Conference : Groups, Rings, and Group Rings, July 28-August 2, 2008, Ubatuba, Brazil / / Antonio Giambruno, César Polcino Milies, Sudarshan K. Sehgal, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2009] |
| Descrizione fisica | 1 online resource (282 p.) |
| Disciplina | 512/.2 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Group theory
Group rings Rings (Algebra) |
| ISBN |
0-8218-8178-7
0-8218-4771-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Contents -- Preface -- The radical of the four generated algebra of alternating type -- Globalization of partial actions on semiprime rings -- The Colombeau quaternion algebra -- Parabolic subgroups of real direct limit Lie groups -- Parabolic sets of roots -- Some results on *-minimal algebras with involution -- Invariants of partial group algebras of finite p-groups -- Units of ZCp -- Algebraic Elements as Free Factors in Simple Artinian Rings -- Special units, unipotent units and free groups in group algebras -- Explicit realizations of simple weight modules of classical Lie superalgebras -- Combinatorial aspects in the computation of proper multiplicities -- An estimate of the dimension of the varieties of alternative and Jordan algebras -- On growth of almost polynilpotent Lie algebras -- Graded identities for Lie algebras -- Polynomial codimension growth of graded algebras -- Euclidean Bianchi groups are conjugacy separable -- Comparability, distributivity and non-commutative Ï?-rings -- Algebras having bases consisting entirely of units -- On the growth of varieties of algebras -- 0-Dialgebras with bar-unity, Rota-Baxter and 3-Leibniz algebras -- The Golod-Shafarevich counterexample without Hilbert series -- Automorphism groups of semi-homogeneous trees. |
| Altri titoli varianti | International Conference : Groups, Rings, and Group Rings, July 28-August 2, 2008, Ubatuba, Brazil |
| Record Nr. | UNINA-9910821759603321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2009] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Polynomial identities in algebras / / edited by Onofrio Mario Di Vincenzo and Antonio Giambruno
| Polynomial identities in algebras / / edited by Onofrio Mario Di Vincenzo and Antonio Giambruno |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (424 pages) : illustrations |
| Disciplina | 512.4 |
| Collana | Springer INdAM |
| Soggetto topico |
PI-algebras
Anells associatius |
| Soggetto genere / forma |
Congressos
Llibres electrònics |
| ISBN | 3-030-63111-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- About the Editors -- Some Thoughts on the Current State of the Theory of Identical Relations in Lie Algebras -- 1 Introduction -- 2 Finite Basis Problem -- 3 Engel Lie Algebras -- 3.1 Global Nilpotence -- 3.2 Restricted Burnside Problem: Local Nilpotence of Engel Lie algebras -- 4 Identities of Simple Lie Algebras -- 4.1 The Isomorphism Problem -- 4.2 Identities of Cartan Type Lie Algebras -- 4.3 Capelli Identities -- 5 Codimension Growth -- 5.1 Exponential Growth -- 5.2 Overexponential Growth -- 5.3 Colength -- 6 Graded Lie Algebras and Identities -- 7 Graded Identities of Lie Algebras and Generalizations -- 7.1 Codimension Growth -- 7.2 Isomorphism of H-Algebras -- 8 Special Lie Algebras -- References -- Minimal Degree of Identities of Matrix Algebras with Additional Structures -- 1 Introduction -- 2 Involution Case -- 3 Graded Case -- 4 Graded Involution Case -- References -- On the Asymptotics of Capelli Polynomials -- 1 Introduction -- 2 Ordinary Case -- 3 Z2-Graded Case -- 4 Involution Case -- 4.1 -Capelli Polynomials and the -Algebra UT(A1, ..., An) -- 4.2 Asymptotics for -Capelli Polynomials -- References -- Regev's Conjecture for Algebras with Hopf Actions -- 1 Introduction -- 2 Regev's Conjectures for Algebras Without Actions -- 2.1 Background on Magnums -- 2.2 Codimension Sequences -- 3 H-Cocharacters -- 4 Rationality of Poincaré Series -- 5 Young Derived Sequences -- References -- -Weak Identities and Central Polynomials for Matrices -- 1 Introduction -- 2 Preliminaries -- 2.1 Identities, Central Polynomials and Examples -- 2.2 Spechtian Polynomials -- 3 Weak Identities -- 3.1 Weak and Strong Variables -- 3.2 Modules of Weak Identities -- 4 Central Polynomials for Matrices -- 4.1 -Weak Central Polynomials -- 5 The Connection to the Representation Theory -- 5.1 Identities and the Group Algebra.
5.2 Identities and Representations -- 6 Weak Identities and the Case n = 2 -- 6.1 Polynomials of Degree m = 2 -- 6.2 Weak Identities of Degree m = 3 -- 6.3 Weak Identities of Degree m = 4 -- 7 The Weak PI-Degree of M3(F) -- 7.1 Fields of Characteristic Not 3 -- 7.2 The Case char F=3 -- 8 Weak Identities for M3(F) in Degree 6 -- 8.1 Weak Identities of M3(F) -- 8.2 Halpin's Identity and Its Projections -- 8.3 Identities from the Okubo Algebra -- 9 Matrices of Size n≥4 -- 9.1 Shadows of Identities -- 9.2 Weak Identities Degree 2n -- References -- Computing Multiplicities in the Sign Trace Cocharacters of M2,1(F) -- 1 Introduction -- 2 Reduced Notation -- 3 The Sign Trace Cocharacter of M2,1(F) -- 3.1 Computation of the Coefficient for {n-2,2} -- 4 The Final Result -- References -- b-Generalized Skew Derivations on Multilinear Polynomials in Prime Rings -- 1 Introduction -- 2 Some Results on Differential Identities with Automorphisms -- 3 Commuting Generalized Derivations and Commuting Generalized Skew Derivations -- 4 Some Remarks on Matrix Algebras -- 5 Commuting Inner b-Generalized Skew Derivations -- 6 Commuting b-Generalized Derivations on Multilinear Polynomials -- 7 The Main Result -- 7.1 Let d and δ be C-Linearly Independent Modulo SDint -- 7.2 Let d and δ be C-Linearly Dependent Modulo SDint -- 8 Some Open Problems -- References -- Relatively Free Algebras of Finite Rank -- 1 Introduction -- 2 Models for Relatively Free Algebras -- 3 General Remarks -- 4 Polynomial Identities for UT2(G(k)) -- 4.1 The Case UT2(G(2m)), for 1≤m≤2 -- 5 Polynomial Identities for Fk(UT2(G)) -- 6 Conclusion -- References -- Graded Algebras, Algebraic Functions, Planar Trees, and Elliptic Integrals -- 1 Introduction -- 2 Growth of Algebras and Hilbert Series -- 3 Algebras with Prescribed Hilbert Series -- 4 PI-Algebras -- 5 Algebraic and Transcendental Power Series. 6 Planar Rooted Trees and Algebraic Series -- 7 Noncommutative Invariant Theory -- References -- Central Polynomials of Algebras and Their Growth -- 1 Introduction -- 2 A General Setting -- 3 Examples of Central Polynomials -- 4 Algebras Without Proper Central Polynomials -- 5 The Proper Central Exponent -- 6 The Central Exponent -- 7 Non Associative Algebras -- References -- Trace Identities on Diagonal Matrix Algebras -- 1 Introduction -- 2 Preliminaries -- 3 Matrix Algebras with Trace -- 4 Some Results on Dn -- 5 Trace Identities on D2 -- 6 Trace Identities on D3 -- References -- Codimension Growth for Weak Polynomial Identities, and Non-integrality of the PI Exponent -- 1 Introduction -- 2 Preliminaries -- 2.1 Generalities -- 2.2 Polynomial Identities -- 2.3 Multilinear Polynomials. Modules over the Symmetric Group -- 2.4 The Exponent -- 2.5 The Action of the General Linear Group -- 2.6 Special Pairs and Pairs of Associative Type -- 3 Polynomial Growth of the Codimensions -- 3.1 Slow Growth of the Codimensions -- 3.2 Characterizing Varieties of Pairs of Polynomial Growth -- 3.3 Almost Polynomial Growth -- 3.3.1 The Pair (UT2,UT2(-)) -- 3.3.2 The Pair (E,E(-)) -- 3.3.3 The Pair (M2,sl2) -- 3.3.4 More Examples -- 4 Graded Pairs and Amitsur's Conjecture -- 4.1 Weak Graded Polynomial Identities -- 4.2 Finitely Generated Superpairs -- 4.3 Non-integral Exponent: An Example -- References -- On Codimensions of Algebras with Involution -- 1 Introduction -- 2 *-Codimensions and *-Fundamental Algebras -- 3 Low Exponential Growth -- References -- Context-Free Languages and Associative Algebras with Algebraic Hilbert Series -- 1 Introduction -- 2 Preliminaries -- 2.1 Associative Algebras and Their Hilbert Series -- 2.2 The Homology and Hilbert Series of Monomial Algebras -- 2.3 Automaton Algebras and Homologically Unambiguous Algebras. 3 Finitely Presented Algebras Associated to Context-Free Languages -- 3.1 The General Construction -- 3.2 Graded Algebras Examples -- References -- On Almost Nilpotent Varieties of Linear Algebras -- 1 Introduction -- 2 Almost Nilpotent Varieties Generated by One or Two Dimensional Algebra -- 3 Almost Nilpotent Varieties and Skew Symmetric Polynomials -- 4 A Commutative Metabelian Algebra with Skew Symmetric Polynomials (a Jordan Algebra) -- 5 Anti-Commutative Metabelian Algebra with Skew Symmetric Polynomials -- 6 A Characterization of Almost Nilpotent Varieties in Different Classes of Algebras -- 7 An Infinite Series of Almost Nilpotent Metabelian Varieties with Polynomial Growth -- 8 Almost Nilpotent Varieties with Exponentional Growth -- References -- (δ,)-Differential Identities of UTm(F) -- 1 Introduction -- 2 The Problem -- 3 The Coupled Actions of δ and on UTm(F) -- 4 The Separate Actions of δ and on UTm(F) -- 5 Behind the Scenes -- References -- Identities in Group Rings, Enveloping Algebras and Poisson Algebras -- 1 Introduction -- 2 Identical Relations of Group Rings -- 3 Identical Relations of Enveloping Algebras -- 4 Poisson Algebras and Their Identities -- 4.1 Poisson Algebras -- 4.2 Examples of Poisson Algebras -- 4.3 Poisson Identities -- 5 Multilinear Identities of Symmetric Poisson Algebras -- 6 Lie Identities of Symmetric Poisson Algebras -- 6.1 Lie Nilpotence of Truncated Symmetric Algebras s(L) -- 6.2 Solvability of Truncated Symmetric Algebras s(L) -- 6.3 Nilpotency and Solvability of Symmetric Algebras S(L) -- 6.4 Delta-Sets and Multilinear Poisson Identical Relations -- 6.5 Products of Commutators in Poisson Algebras -- 6.6 Solvability of Symmetric Algebras s(L) and S(L) in Case Char K = 2 -- References -- Notes on the History of Identities on Group (and Loop) Algebras -- 1 Introduction. 2 Existence of Polynomial Identities -- 3 Group Theoretical Properties of Unit Groups -- 4 Group Indentities -- 5 Loop Algebras -- References -- Cayley Hamilton Algebras -- 1 Introduction -- 2 The Cayley-Hamilton Identity -- 3 The First and Second Fundamental Theorem -- 3.1 The Free Trace Algebra -- 3.3 A Characteristic Free Approach -- 3.12 Symbolic Approach -- 3.12.1 The Approach of Zieplies and Vaccarino -- References -- Growth of Differential Identities -- 1 Introduction -- 2 L-Algebras and Differential Identities -- 3 On Algebras with Derivations of Polynomial Growth -- 4 The Algebra of 2 x 2 Upper Triangular Matrices and Its Differential Identities -- 5 On Differential Identities of the Grassmann Algebra -- References -- Derived Lengths of Symmetric Poisson Algebras -- 1 Introduction -- 2 Definitions and Notation -- 3 The Lie Structure of Enveloping Algebras -- 4 Symmetric Poisson Algebras Satisfying a Poisson Identity -- 5 Lie Nilpotence and Solvability of S(L) and s(L) -- 6 Derived Lengths of s(L) -- References -- Group and Polynomial Identities in Group Rings -- 1 Introduction -- 2 -Group Identities for U(FG) -- 3 Group Identities for Unitary Units of FG -- References. |
| Record Nr. | UNISA-996466544303316 |
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Polynomial identities in algebras / / edited by Onofrio Mario Di Vincenzo and Antonio Giambruno
| Polynomial identities in algebras / / edited by Onofrio Mario Di Vincenzo and Antonio Giambruno |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (424 pages) : illustrations |
| Disciplina | 512.4 |
| Collana | Springer INdAM |
| Soggetto topico |
PI-algebras
Anells associatius |
| Soggetto genere / forma |
Congressos
Llibres electrònics |
| ISBN | 3-030-63111-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- About the Editors -- Some Thoughts on the Current State of the Theory of Identical Relations in Lie Algebras -- 1 Introduction -- 2 Finite Basis Problem -- 3 Engel Lie Algebras -- 3.1 Global Nilpotence -- 3.2 Restricted Burnside Problem: Local Nilpotence of Engel Lie algebras -- 4 Identities of Simple Lie Algebras -- 4.1 The Isomorphism Problem -- 4.2 Identities of Cartan Type Lie Algebras -- 4.3 Capelli Identities -- 5 Codimension Growth -- 5.1 Exponential Growth -- 5.2 Overexponential Growth -- 5.3 Colength -- 6 Graded Lie Algebras and Identities -- 7 Graded Identities of Lie Algebras and Generalizations -- 7.1 Codimension Growth -- 7.2 Isomorphism of H-Algebras -- 8 Special Lie Algebras -- References -- Minimal Degree of Identities of Matrix Algebras with Additional Structures -- 1 Introduction -- 2 Involution Case -- 3 Graded Case -- 4 Graded Involution Case -- References -- On the Asymptotics of Capelli Polynomials -- 1 Introduction -- 2 Ordinary Case -- 3 Z2-Graded Case -- 4 Involution Case -- 4.1 -Capelli Polynomials and the -Algebra UT(A1, ..., An) -- 4.2 Asymptotics for -Capelli Polynomials -- References -- Regev's Conjecture for Algebras with Hopf Actions -- 1 Introduction -- 2 Regev's Conjectures for Algebras Without Actions -- 2.1 Background on Magnums -- 2.2 Codimension Sequences -- 3 H-Cocharacters -- 4 Rationality of Poincaré Series -- 5 Young Derived Sequences -- References -- -Weak Identities and Central Polynomials for Matrices -- 1 Introduction -- 2 Preliminaries -- 2.1 Identities, Central Polynomials and Examples -- 2.2 Spechtian Polynomials -- 3 Weak Identities -- 3.1 Weak and Strong Variables -- 3.2 Modules of Weak Identities -- 4 Central Polynomials for Matrices -- 4.1 -Weak Central Polynomials -- 5 The Connection to the Representation Theory -- 5.1 Identities and the Group Algebra.
5.2 Identities and Representations -- 6 Weak Identities and the Case n = 2 -- 6.1 Polynomials of Degree m = 2 -- 6.2 Weak Identities of Degree m = 3 -- 6.3 Weak Identities of Degree m = 4 -- 7 The Weak PI-Degree of M3(F) -- 7.1 Fields of Characteristic Not 3 -- 7.2 The Case char F=3 -- 8 Weak Identities for M3(F) in Degree 6 -- 8.1 Weak Identities of M3(F) -- 8.2 Halpin's Identity and Its Projections -- 8.3 Identities from the Okubo Algebra -- 9 Matrices of Size n≥4 -- 9.1 Shadows of Identities -- 9.2 Weak Identities Degree 2n -- References -- Computing Multiplicities in the Sign Trace Cocharacters of M2,1(F) -- 1 Introduction -- 2 Reduced Notation -- 3 The Sign Trace Cocharacter of M2,1(F) -- 3.1 Computation of the Coefficient for {n-2,2} -- 4 The Final Result -- References -- b-Generalized Skew Derivations on Multilinear Polynomials in Prime Rings -- 1 Introduction -- 2 Some Results on Differential Identities with Automorphisms -- 3 Commuting Generalized Derivations and Commuting Generalized Skew Derivations -- 4 Some Remarks on Matrix Algebras -- 5 Commuting Inner b-Generalized Skew Derivations -- 6 Commuting b-Generalized Derivations on Multilinear Polynomials -- 7 The Main Result -- 7.1 Let d and δ be C-Linearly Independent Modulo SDint -- 7.2 Let d and δ be C-Linearly Dependent Modulo SDint -- 8 Some Open Problems -- References -- Relatively Free Algebras of Finite Rank -- 1 Introduction -- 2 Models for Relatively Free Algebras -- 3 General Remarks -- 4 Polynomial Identities for UT2(G(k)) -- 4.1 The Case UT2(G(2m)), for 1≤m≤2 -- 5 Polynomial Identities for Fk(UT2(G)) -- 6 Conclusion -- References -- Graded Algebras, Algebraic Functions, Planar Trees, and Elliptic Integrals -- 1 Introduction -- 2 Growth of Algebras and Hilbert Series -- 3 Algebras with Prescribed Hilbert Series -- 4 PI-Algebras -- 5 Algebraic and Transcendental Power Series. 6 Planar Rooted Trees and Algebraic Series -- 7 Noncommutative Invariant Theory -- References -- Central Polynomials of Algebras and Their Growth -- 1 Introduction -- 2 A General Setting -- 3 Examples of Central Polynomials -- 4 Algebras Without Proper Central Polynomials -- 5 The Proper Central Exponent -- 6 The Central Exponent -- 7 Non Associative Algebras -- References -- Trace Identities on Diagonal Matrix Algebras -- 1 Introduction -- 2 Preliminaries -- 3 Matrix Algebras with Trace -- 4 Some Results on Dn -- 5 Trace Identities on D2 -- 6 Trace Identities on D3 -- References -- Codimension Growth for Weak Polynomial Identities, and Non-integrality of the PI Exponent -- 1 Introduction -- 2 Preliminaries -- 2.1 Generalities -- 2.2 Polynomial Identities -- 2.3 Multilinear Polynomials. Modules over the Symmetric Group -- 2.4 The Exponent -- 2.5 The Action of the General Linear Group -- 2.6 Special Pairs and Pairs of Associative Type -- 3 Polynomial Growth of the Codimensions -- 3.1 Slow Growth of the Codimensions -- 3.2 Characterizing Varieties of Pairs of Polynomial Growth -- 3.3 Almost Polynomial Growth -- 3.3.1 The Pair (UT2,UT2(-)) -- 3.3.2 The Pair (E,E(-)) -- 3.3.3 The Pair (M2,sl2) -- 3.3.4 More Examples -- 4 Graded Pairs and Amitsur's Conjecture -- 4.1 Weak Graded Polynomial Identities -- 4.2 Finitely Generated Superpairs -- 4.3 Non-integral Exponent: An Example -- References -- On Codimensions of Algebras with Involution -- 1 Introduction -- 2 *-Codimensions and *-Fundamental Algebras -- 3 Low Exponential Growth -- References -- Context-Free Languages and Associative Algebras with Algebraic Hilbert Series -- 1 Introduction -- 2 Preliminaries -- 2.1 Associative Algebras and Their Hilbert Series -- 2.2 The Homology and Hilbert Series of Monomial Algebras -- 2.3 Automaton Algebras and Homologically Unambiguous Algebras. 3 Finitely Presented Algebras Associated to Context-Free Languages -- 3.1 The General Construction -- 3.2 Graded Algebras Examples -- References -- On Almost Nilpotent Varieties of Linear Algebras -- 1 Introduction -- 2 Almost Nilpotent Varieties Generated by One or Two Dimensional Algebra -- 3 Almost Nilpotent Varieties and Skew Symmetric Polynomials -- 4 A Commutative Metabelian Algebra with Skew Symmetric Polynomials (a Jordan Algebra) -- 5 Anti-Commutative Metabelian Algebra with Skew Symmetric Polynomials -- 6 A Characterization of Almost Nilpotent Varieties in Different Classes of Algebras -- 7 An Infinite Series of Almost Nilpotent Metabelian Varieties with Polynomial Growth -- 8 Almost Nilpotent Varieties with Exponentional Growth -- References -- (δ,)-Differential Identities of UTm(F) -- 1 Introduction -- 2 The Problem -- 3 The Coupled Actions of δ and on UTm(F) -- 4 The Separate Actions of δ and on UTm(F) -- 5 Behind the Scenes -- References -- Identities in Group Rings, Enveloping Algebras and Poisson Algebras -- 1 Introduction -- 2 Identical Relations of Group Rings -- 3 Identical Relations of Enveloping Algebras -- 4 Poisson Algebras and Their Identities -- 4.1 Poisson Algebras -- 4.2 Examples of Poisson Algebras -- 4.3 Poisson Identities -- 5 Multilinear Identities of Symmetric Poisson Algebras -- 6 Lie Identities of Symmetric Poisson Algebras -- 6.1 Lie Nilpotence of Truncated Symmetric Algebras s(L) -- 6.2 Solvability of Truncated Symmetric Algebras s(L) -- 6.3 Nilpotency and Solvability of Symmetric Algebras S(L) -- 6.4 Delta-Sets and Multilinear Poisson Identical Relations -- 6.5 Products of Commutators in Poisson Algebras -- 6.6 Solvability of Symmetric Algebras s(L) and S(L) in Case Char K = 2 -- References -- Notes on the History of Identities on Group (and Loop) Algebras -- 1 Introduction. 2 Existence of Polynomial Identities -- 3 Group Theoretical Properties of Unit Groups -- 4 Group Indentities -- 5 Loop Algebras -- References -- Cayley Hamilton Algebras -- 1 Introduction -- 2 The Cayley-Hamilton Identity -- 3 The First and Second Fundamental Theorem -- 3.1 The Free Trace Algebra -- 3.3 A Characteristic Free Approach -- 3.12 Symbolic Approach -- 3.12.1 The Approach of Zieplies and Vaccarino -- References -- Growth of Differential Identities -- 1 Introduction -- 2 L-Algebras and Differential Identities -- 3 On Algebras with Derivations of Polynomial Growth -- 4 The Algebra of 2 x 2 Upper Triangular Matrices and Its Differential Identities -- 5 On Differential Identities of the Grassmann Algebra -- References -- Derived Lengths of Symmetric Poisson Algebras -- 1 Introduction -- 2 Definitions and Notation -- 3 The Lie Structure of Enveloping Algebras -- 4 Symmetric Poisson Algebras Satisfying a Poisson Identity -- 5 Lie Nilpotence and Solvability of S(L) and s(L) -- 6 Derived Lengths of s(L) -- References -- Group and Polynomial Identities in Group Rings -- 1 Introduction -- 2 -Group Identities for U(FG) -- 3 Group Identities for Unitary Units of FG -- References. |
| Record Nr. | UNINA-9910484534203321 |
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||