Skip to main content
Kent Academic Repository

Depth and cohomological connectivity in modular invariant theory

Fleischmann, Peter, Kemper, Gregor, 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. (doi:10.1090/S0002-9947-04-03591-3) (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) (KAR id:520)

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.
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
DOI/Identification number: 10.1090/S0002-9947-04-03591-3
Uncontrolled keywords: Rings
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Judith Broom
Date Deposited: 19 Dec 2007 18:18 UTC
Last Modified: 16 Nov 2021 09:39 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/520 (The current URI for this page, for reference purposes)

University of Kent Author Information

Fleischmann, Peter.

Creator's ORCID:
CReDIT Contributor Roles:

Shank, R. James.

Creator's ORCID: https://orcid.org/0000-0002-3317-4088
CReDIT Contributor Roles:
  • Depositors only (login required):

Total unique views for this document in KAR since July 2020. For more details click on the image.