Polynomial Identities and Combinatorial Methods presents a wide range of perspectives on topics ranging from ring theory and combinatorics to invariant theory and associative algebras. It covers recent breakthroughs and strategies impacting research on polynomial identities and identifies new concepts in algebraic combinatorics, invariant and representation theory, and Lie algebras and superalgebras for novel studies in the field. It presents intensive discussions on various methods and techniques relating the theory of polynomial identities to other branches of algebraic study and includes discussions on Hopf algebras and quantum polynomials, free algebras and Scheier varieties.
Table of Contents
Preface, Contributors, 1. Linearization Method of Computing Z2-Codimensions of Identities of the Grassmann Algebra, 2. Cocommutative Hopf Algebras Acting on Quantum Polynomials and Their Invariants, 3. Combinatorial Properties of Free Algebras of Schreier Varieties, 4. Graded Algebras and Graded Identities, 5. Computational Approach to Polynomial Identities of Matrices: A Survey, 6. Poincare Series of Generic Matrices, 7. Combinatorial Methods for the Computation of Trace Cocharacters, 8. Polynomial Identities for Graded Algebras, 9. Matrix Invariants and the Failure of Weyl's Theorem, 10. Free Nilpotent-by-Abelian Leibniz Algebras, 11. Pebbles and Expansions in the Polynomial Ring, 12. Group Actions, Codimensions, and Exponential Behaviour, 13. Monotone Matrix Maps Preserve Non-maximal Rank, 14. Explicit Decompositions of the Group Algebras FS, and FA, 15. Graded and Ordinary Polynomial Identities in Matrix and Related Algebras, 16. Varieties of Linear Algebras with Almost Polynomial Growth, 17. Algebras with Involution, Superalgebras, and Proper Subvarieties, 18. Gradings and Graded Identities of the Algebra of n x n Upper Triangular Matrices
Giambruno\, Antonio Unisersita Di Palermo Italy,; Regev\, Amitai; Zaicev\, Mikhail State University of Russia.