Polynomial identities in algebras / Onofrio Mario Di Vincenzo, Antonio Giambruno, editors.

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 ne."

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