The module structure of a group action on a polynomial ring: A finiteness theorem

Karagueuzian, Dikran B. and Symonds, Peter (2007) The module structure of a group action on a polynomial ring: A finiteness theorem. Journal of the American Mathematical Society, 20 (4). pp. 931-967. ISSN 1088-6834

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Abstract

Consider a group acting on a polynomial ring over a finite field. We study the polynomial ring as a module for the group and prove a structure theorem with several striking corollaries. For example, any indecomposable module that appears as a summand must also appear in low degree, and so the number of isomorphism types of such summands is finite. There are also applications to invariant theory, giving a priori bounds on the degrees of the generators.

Item Type:	Article
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User:	Ms Lucy van Russelt
Date Deposited:	20 Nov 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/929

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