\(Y\)-proper graded cocharacters and codimensions of upper triangular matrices of size 2, 3, 4.
type: Item
instance of: scholarly article
title: \(Y\)-proper graded cocharacters and codimensions of upper triangular matrices of size 2, 3, 4.
zbMATH Open document ID: 1279.16018
author: Lucio Centrone
author: Alessio Cirrito
published in: Journal of Algebra
publication date: 2013-04-22T00:00:00Z
review text: The authors consider graded polynomial identities of algebras over a field of characteristic 0. The algebras of upper triangular matrices play an important role in PI theory, and they are object of an extensive study. The graded identities of these algebras are of interest due to the extremal properties of the polynomial identities of upper triangular matrices. The main results in the paper under review consist in describing the graded codimensions and cocharacters for the upper triangular matrices of order up to 4. The authors give explicit formulae for the graded \(Y\)-proper codimensions and cocharacters (and their multiplicities). Here \(Y\) stands for the variables in the free graded associative algebra that are of degree 1 in the grading (the group being multiplicative).
Mathematics Subject Classification ID: 16R10
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 20C30
zbMATH DE Number: 6156191
zbMATH Keywords: polynomial identities
zbMATH Keywords: graded identities
zbMATH Keywords: upper triangular matrix algebras
zbMATH Keywords: graded codimensions
zbMATH Keywords: graded cocharacters
reviewed by: Plamen Koshlukov
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2012.05.019
OpenAlex ID: W1983585818
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DOI: 10.1016/J.JALGEBRA.2012.05.019
description: scientific article; zbMATH DE number 6156191