Linear groups associated with elements of a group algebra
type: Item
instance of: scholarly article
title: Linear groups associated with elements of a group algebra
zbMATH Open document ID: 0629.20019
DOI: 10.1016/0024-3795(87)90087-5
author: J. A. Dias Da Silva
author: Maria da Purificação Coelho
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: Let K be a field, \(M_ m(K)\) the \(m\times m\) matrices with entries in K, and \(S_ m\) the symmetric group of degree m. If c is a function from \(S_ m\) to K, let \(d_ c(A)=\sum_{\sigma \in S_ m}c(\sigma)\prod^{m}_{i=1}A_{i,\sigma (i)}\) and let S(c) be the group of non-singular matrices B satisfying \(d_ c(BX)=d_ c(X)\) for all \(X\in M_ m(K)\). S(c) gives information about the problem of determining conditions for equality of decomposible symmetric tensors. The authors give necessary and sufficient conditions for a matrix to belong to S(c). In addition, they find properties that matrices which belong to S(c) satisfy.
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 16Dxx
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 4023562
zbMATH Keywords: symmetric group
zbMATH Keywords: group of non-singular matrices
zbMATH Keywords: decomposible symmetric tensors
reviewed by: E. Spiegel
MaRDI profile type: Publication
full work available at URL: 0024-3795(87)90087-5
OpenAlex ID: W2062857965
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description: scientific article; zbMATH DE number 4023562