Depth and cohomological connectivity in modular invariant theory

Fleischmann, P. and Kemper, G. and Shank, RJ (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 available from this repository)

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Official URL
http://dx.doi.org/10.1090/S0002-9947-04-03591-3

Abstract

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: 14 Jan 2010 13:58
Resource URI: http://kar.kent.ac.uk/id/eprint/520 (The current URI for this page, for reference purposes)
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