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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