Non-Cohen-Macaulay invariant rings of infinite groups
type: Item
instance of: scholarly article
title: Non-Cohen-Macaulay invariant rings of infinite groups
zbMATH Open document ID: 1107.13008
author: Martin Kohls
published in: Journal of Algebra
publication date: 2007-01-11T00:00:00Z
review text: Let \(K\) be an algebraically closed field of positive characteristic. In this paper there are given some explicit examples of invariant rings that are not Cohen-Macaulay for all classical groups SL\(_{n}(K)\), GL\(_{n}(K)\), Sp\(_{2n}(K) \), SO\(_{n}(K)\) and O\(_{n}(K)\). It is also proved that every non-trivial unipotent group over \(K\) has representations such that the invariant ring is not Cohen-Macaulay (see Section 4). All results of the paper are new and carefully proved. The manner of presenting is clear, with many examples, and so the paper contributes to the development of this important research domain.
Mathematics Subject Classification ID: 13A50
zbMATH DE Number: 5115360
reviewed by: Marius Tărnăuceanu
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2006.03.028
OpenAlex ID: W2041275443
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DOI: 10.1016/J.JALGEBRA.2006.03.028
description: scientific article; zbMATH DE number 5115360