On the depth of separating algebras for finite groups
type: Item
instance of: scholarly article
title: On the depth of separating algebras for finite groups
zbMATH Open document ID: 1241.13008
author: Jon Elmer
published in: Beiträge zur Algebra und Geometrie
publication date: 2012-02-29T00:00:00Z
review text: Let \(G\) be a finite group acting linearly on a finite dimensional vector space \(V\) over a field \(k\). It is well known that when the characteristic of \(k\) divides the order of \(G\), the ring of invariants \(k[V]^G\) is not necessarily Cohen-Macaulay. This was strengthened recently by \textit{J. Elmer, E. Dufresne} and \textit{M. Kohls} [Transform. Groups 14, 771--785 (2009; Zbl 1184.13019)] who gave conditions guaranteeing that \(k[V]^G\) does not even contains a Cohen-Macaulay separating subalgebra. The present work is a sequel to that providing some refinements. It is shown here that under certain structural conditions on \(G\), the depth of any separating subalgebra is bounded from above by the depth of \(k[V]^G\).
reviewed by: Matyas Domokos
Mathematics Subject Classification ID: 13A50
zbMATH DE Number: 6010032
zbMATH Keywords: invariant theory
zbMATH Keywords: separating algebra
zbMATH Keywords: depth
zbMATH Keywords: modular representation theory
zbMATH Keywords: cohomology modules
MaRDI profile type: Publication
full work available at URL: s13366-011-0030-1
OpenAlex ID: W1993843139
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DOI: 10.1007/S13366-011-0030-1
description: scientific article; zbMATH DE number 6010032