Depth and cohomological connectivity in modular invariant theory

Fleischmann, Peter and Kemper, Gregor and Shank, R. James (2005) Depth and cohomological connectivity in modular invariant theory. Transactions of the American Mathematical Society, 357 (9). pp. 3605-3621. ISSN 0002-9947. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Let G be a finite group acting linearly on a finite-dimensional vector space V over a field K of characteristic p. Assume that p divides the order of G so that V is a modular representation and let P be a Sylow p-subgroup for G. De. ne the cohomological connectivity of the symmetric algebra S( V *) to be the smallest positive integer m such that H-m( G, S( V *)) not equal 0. We show that min {dim(K)(V-P) + m+ 1, dim(K)( V)} is a lower bound for the depth of S( V *) G. We characterize those representations for which the lower bound is sharp and give several examples of representations satisfying the criterion. In particular, we show that if G is p-nilpotent and P is cyclic, then, for any modular representation, the depth of S( V *) G is min {dim(K)(V-P) + 2, dim(K)(V)}.

Item Type: Article
Uncontrolled keywords: Rings
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Judith Broom
Date Deposited: 19 Dec 2007 18:18
Last Modified: 19 May 2014 13:27
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