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

Book chapter


Elmer, J. and Fleischmann, P. 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 Birkhauser Boston.
Chapter titleOn the depth of modular invariant rings for the groups C_p x C_p
AuthorsElmer, J. and Fleischmann, P.
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.

LanguageEnglish
Book titleSymmetry and Spaces: in honour of Gerry Schwarz
PublisherBirkhauser Boston
SeriesProgress in Mathematics
ISBN
Hardcover9780817648749
Publication dates
Print14 Nov 2009
Publication process dates
Deposited14 Apr 2016
Output statusPublished
Copyright Statement

Access to full text restricted pending copyright check

Digital Object Identifier (DOI)https://doi.org/10.1007/978-0-8176-4875-6_4
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