Polynomial Identities and Combinatorial Methods

by Giambruno; Antonio

• ISBN13: 9780824740511
• ISBN10: 0824740513
• Format: Paperback
• Copyright: 2003-05-20
• Publisher: CRC Press

Summary

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	iii
Contributors	vii
Linearization Method of Computing Z2-Codimensions of Identities of the Grassmann Algebra	1	(26)
N. Anisimov
Cocommutative Hopf Algebras Acting on Quantum Polynomials and Their Invariants	27	(20)
Vyacheslav A. Artamonov
Combinatorial Properties of Free Algebras of Schreier Varieties	47	(54)
Vyacheslav A. Artamonov
Alexander A. Mikhalev
Alexander V. Mikhalev
Graded Algebras and Graded Identities	101	(40)
Yu. A. Bahturin
M. V. Zaicev
Computational Approach to Polynomial Identities of Matrices: A Survey	141	(38)
Francesca Benanti
James Demmel
Vesselin Drensky
Plamen Koev
Poincare Series of Generic Matrices	179	(14)
Allan Berele
Combinatorial Methods for the Computation of Trace Cocharacters	193	(10)
Luisa Carini
Polynomial Identities for Graded Algebras	203	(12)
Onofrio Mario Di Vincenzo
Matrix Invariants and the Failure of Weyl's Theorem	215	(22)
M. Domokos
Free Nilpotent-by-Abelian Leibniz Algebras	237	(24)
Vesselin Drensky
Giulia Maria Piacentini Cattaneo
Pebbles and Expansions in the Polynomial Ring	261	(26)
Adriano M. Garsia
Group Actions, Codimensions, and Exponential Behaviour	287	(24)
A. Giambruno
Monotone Matrix Maps Preserve Non-maximal Rank	311	(18)
A. Guterman
Explicit Decompositions of the Group Algebras FSn and FAn	329	(30)
A. Henke
A. Regev
Graded and Ordinary Polynomial Identities in Matrix and Related Algebras	359	(24)
Plamen Koshlukov
Varieties of Linear Algebras with Almost Polynomial Growth	383	(14)
S. P. Mishchenko
Algebras with Involution, Superalgebras, and Proper Subvarieties	397	(12)
Vincenzo Nardozza
Gradings and Graded Identities of the Algebras of n x n Upper Triangular Matrices	409
Angela Valenti