Invariants of finite linear groups on relatively free algebras
type: Item
instance of: scholarly article
title: Invariants of finite linear groups on relatively free algebras
zbMATH Open document ID: 0579.20039
DOI: 10.1016/0024-3795(85)90144-2
author: Robert Guralnick
published in: Linear Algebra and its Applications
publication date: 1985-01-01T00:00:00Z
review text: Extend the action of a finite group G on a finite dimensional vector space V over an infinite field F to the tensor algebra F(V). The ring R of \(n\times n\) generic matrices over F [on \(d>1\) generators] is defined to be \(F<V>\) factored out by the ideal of identities satisfied by \(n\times n\) matrices over F. If n and the dimension of V are both greater than 1 and F is of characteristic 0, then \(R^ G\) cannot be generated by d elements as an F-algebra. In particular \(R^ G\) is not isomorphic to a ring of generic matrices. Very early in the proof the reduction is made to the case that G is a quasireflection group acting irreducibly on V.
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 16Rxx
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 20G35
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 3927208
zbMATH Keywords: action of a finite group
zbMATH Keywords: finite dimensional vector space
zbMATH Keywords: tensor algebra
zbMATH Keywords: ideal of identities
zbMATH Keywords: ring of generic matrices
zbMATH Keywords: quasireflection group
MaRDI profile type: Publication
full work available at URL: 0024-3795(85)90144-2
OpenAlex ID: W1984005855
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description: scientific article; zbMATH DE number 3927208