Permutability of characters on algebras
type: Item
instance of: scholarly article
title: Permutability of characters on algebras
zbMATH Open document ID: 0891.16023
published in: Pacific Journal of Mathematics
publication date: 1998-07-12T00:00:00Z
review text: Let \(A\) be a subalgebra of \(M_n(F)\) where \(F\) is a field. \(A\) has permutable trace if the traces \(\text{tr}(abc)\) and \(\text{tr}(bac)\) are equal for any matrices \(a,b,c\in A\). The authors prove the following main results: i) Let the characteristic of \(F\) be either zero or \(p\) and \(n<2p\). Then \(A\) has permutable trace if and only if \(A/J(A)\) is commutative (\(J(A)\) is the Jacobson radical of \(A\)); ii) Let the trace form on \(A\), defined by \((a,b)=\text{tr}(ab)\) be non-degenerate. Then the trace is permutable if and only if \(A/J(A)\) is commutative; iii) Let the characteristic of \(F\) be non zero. Then \(A\) has permutable Brauer character if and only if \(A/J(A)\) is commutative.
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A27
zbMATH DE Number: 1054048
zbMATH Keywords: permutable traces
zbMATH Keywords: matrices
zbMATH Keywords: Jacobson radical
zbMATH Keywords: trace forms
zbMATH Keywords: permutable Brauer characters
author: L. Grunenfelder
author: Robert Guralnick
author: T. Košir
author: H. Radjavi
reviewed by: Yu. N. Maltsev
MaRDI profile type: Publication
full work available at URL: pjm.1997.178.63
OpenAlex ID: W2150705315
DOI: 10.2140/PJM.1997.178.63
description: scientific article; zbMATH DE number 1054048