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. [Book Section] (doi:10.1007/978-0-8176-4875-6_4)

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Abstract

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
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Depositing User: Jonathan Elmer
Date Deposited: 14 Apr 2016 13:54
Last Modified: 24 Jun 2021 15:21
URI: https://eprints.mdx.ac.uk/id/eprint/19268

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