On the depth of modular invariant rings for the groups C_p x C_p

Elmer, Jonathan ORCID: https://orcid.org/0000-0001-5296-1987 and Fleischmann, Peter (2009) On the depth of modular invariant rings for the groups C_p x C_p. In: Symmetry and Spaces: in honour of Gerry Schwarz. Progress in Mathematics (278) . Birkhauser Boston, pp. 45-61. ISBN 9780817648749. (doi:10.1007/978-0-8176-4875-6_4)

[img] PDF - Final accepted version (with author's formatting)
Restricted to Repository staff and depositor only

Download (166kB)


Let G be a finite group, k a field of characteristic p and V a finite dimensional kG-module. Let R denote the symmetric algebra over the dual space V∗ with G acting by graded algebra automorphisms. Then it is known that the depth of the invariant ring R^G is at least min {dim(V), dim(V^P)+cc_G(R)+1}. A module V for which the depth of R^G 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 C_p × C_p, generating many new examples of flat modules. We introduce the useful notion of “strongly flat” modules, classi-fying them for the group C_2 × C_2, as well as determining the depth of R^G for any indecomposable modular representation of C_2 × C_2.

Item Type: Book Section
Research Areas: A. > School of Science and Technology > Design Engineering and Mathematics
Item ID: 19268
Notes on copyright: Access to full text restricted pending copyright check
Useful Links:
Depositing User: Jonathan Elmer
Date Deposited: 14 Apr 2016 13:54
Last Modified: 15 Oct 2019 05:14
URI: https://eprints.mdx.ac.uk/id/eprint/19268

Actions (login required)

Edit Item Edit Item

Full text downloads (NB count will be zero if no full text documents are attached to the record)

Downloads per month over the past year