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2007.184: The module structure of a group action on a polynomial ring: A finiteness theorem

2007.184: Dikran B. Karagueuzian and Peter Symonds (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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DOI: 10.1090/S0894-0347-07-00563-2

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 2000 > 16 Associative rings and algebras
MSC 2000 > 20 Group theory and generalizations
MIMS number:2007.184
Deposited By:Mrs Louise Healey
Deposited On:20 November 2007

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