Some remarks on trace cocharacters
type: Item
instance of: scholarly article
title: Some remarks on trace cocharacters
zbMATH Open document ID: 0838.16016
author: Allan Berele
author: Amitai Regev
published in: Journal of Algebra
publication date: 1996-05-28T00:00:00Z
review text: The cocharacter sequences are one of the important numerical characteristics of a PI algebra. There are many connections between the cocharacters and the trace cocharacters, and it is often desirable to pass from one to the other in order to avoid complicated calculations. The authors study the pure and the mixed trace cocharacters of algebras over a field of characteristic zero. First they show that the cocharacter sequences are Young derived if the algebra is unitary PI with nonzero trace. In addition the pure trace cocharacter sequence is not twice Young derived while the mixed one is not triple Young derived. Then the algebras \(M_{k,l}\) are considered. They are an important example for the above results. It turns out that when \(k\neq l\) the mixed trace cocharacters are Young derived, and when \(k=l\) they are not Young derived. Some other important applications (both structural and combinatorial) are made for the cocharacters of the algebra of all diagonal \(n\times n\) matrices as well as of the algebra of all upper triangular \(2\times 2\) matrices.
Mathematics Subject Classification ID: 16R20
Mathematics Subject Classification ID: 16R30
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 05E05
zbMATH DE Number: 815880
zbMATH Keywords: verbally prime algebras
zbMATH Keywords: Young derived series
zbMATH Keywords: cocharacter sequences
zbMATH Keywords: PI algebras
zbMATH Keywords: trace cocharacters
zbMATH Keywords: mixed trace cocharacters
zbMATH Keywords: diagonal \(n\times n\) matrices
zbMATH Keywords: upper triangular \(2\times 2\) matrices
reviewed by: Plamen Koshlukov
MaRDI profile type: Publication
full work available at URL: jabr.1995.1282
OpenAlex ID: W1964646220
DOI: 10.1006/JABR.1995.1282
description: scientific article; zbMATH DE number 815880