Projective Schur algebras have Abelian splitting fields
type: Item
instance of: scholarly article
title: Projective Schur algebras have Abelian splitting fields
zbMATH Open document ID: 0828.16017
author: Eli Aljadeff
author: Jack Sonn
published in: Journal of Algebra
publication date: 1995-12-18T00:00:00Z
review text: For any commutative ring \(R\), a Schur algebra \(A\) is an Azumaya \(R\)- algebra for which there is a finite group \(G\) and an \(R\)-algebra epimorphism \(f:RG\to A\). This was the generalization of the notion of a Schur algebra given and studied by \textit{F. DeMeyer} and \textit{R. Mollin} [in J. Pure Appl. Algebra 35, 117-122 (1985; Zbl 0555.13003)]. The paper under review restricts attention to the field case and the generalization of the Schur algebras to projective Schur algebras. The main result of their paper is the predictable fact that every projective Schur algebra over a field \(K\) is split by an abelian extension of \(K\). It would be interesting to investigate whether or not this holds true in the more general ring case, using theory as given for example by \textit{F. DeMeyer} and \textit{E. Ingraham} [in Separable algebras over commutative rings (Lect. Notes Math. 181, 1971; Zbl 0215.366)].
Mathematics Subject Classification ID: 16K20
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 14F22
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 783917
zbMATH Keywords: Azumaya algebras
zbMATH Keywords: finite groups
zbMATH Keywords: Schur algebras
zbMATH Keywords: projective Schur algebras
reviewed by: Richard A. Mollin
MaRDI profile type: Publication
full work available at URL: jabr.1995.1181
OpenAlex ID: W2090984406
DOI: 10.1006/JABR.1995.1181
description: scientific article; zbMATH DE number 783917