On the Depth of Modular Invariant Rings for the Groups Cp x Cp

Elmer, Jonathan and Fleischmann, Peter (2010) On the Depth of Modular Invariant Rings for the Groups Cp x Cp. In: Campbell, Eddy and Helminck, Aloysius G. and Hanspeter, Kraft and Wehlau, David L., eds. Symmetry and Spaces: In Honor of Gerry Schwarz. Progress in Mathematics , 278 . Birkhäuser, Boston, pp. 45-61. ISBN 9780817648749. (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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Official URL
http://dx.doi.org/10.1007/978-0-8176-4875-6

Abstract

Let G be a finite group, k a field of characteristic p and V a finite dimen- sional kG-module. Let R :=Sym(V�), the symmetric algebra over the dual spaceV�, with G acting by graded algebra automorphisms. Then it is known that the depth of the invariant ring RG is at least min{dim(V),dim(VP)+ccG(R)+1}. A module V for which the depth of RG attains this lower bound was called flat by Fleischmann, Kemper and Shank [13]. In this paper some of the ideas in [13] are further developed and applied to certain representations of Cp ×Cp, generating many new examples of flat modules. We introduce the useful notion of “strongly flat” modules, classi- fying them for the group C2 ×C2, as well as determining the depth of RG for any indecomposable modular representation of C2×C2.

Item Type: Book section
Subjects: Q Science > QA Mathematics (inc Computing science) > QA150 Algebra
Q Science > QA Mathematics (inc Computing science) > QA171 Representation theory
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Peter Fleischmann
Date Deposited: 11 Oct 2012 11:25
Last Modified: 09 Jul 2014 09:42
Resource URI: https://kar.kent.ac.uk/id/eprint/31524 (The current URI for this page, for reference purposes)
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