# 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 978-0-8176-4874-9. (doi:10.1007/978-0-8176-4875-6) (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:31524)

 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 URLhttp://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 10.1007/978-0-8176-4875-6 Q Science > QA Mathematics (inc Computing science) > QA150 AlgebraQ Science > QA Mathematics (inc Computing science) > QA171 Representation theory Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science Peter Fleischmann 11 Oct 2012 11:25 UTC 16 Nov 2021 10:09 UTC https://kar.kent.ac.uk/id/eprint/31524 (The current URI for this page, for reference purposes)