On the Depth of Modular Invariant Rings for the GroupsCp×Cp

JP Elmer, P Fleischmann

Research output: Chapter in Book/Report/Conference proceedingChapter in a book


Let G be a finite group, k a field of characteristic p and V a finite dimensional 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 f “strongly flat” modules, classifying them for the group C2 ×C2, as well as determining the depth of RG for any indecomposable modular representation of C2×C2.
Translated title of the contributionOn the Depth of Modular Invariant Rings for the GroupsCp×Cp
Original languageEnglish
Title of host publicationSymmetry and Spaces
EditorsCampbell , H.E.A.E.; Helminck, A.G.; Kraft, D.L H.; Wehlau
Pages45 - 63
Number of pages13
ISBN (Print)9780817648749
Publication statusPublished - 2010

Bibliographical note

Other: Progress in Mathematics, vol 278


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