@inbook{bf054db77b5f471ab19adbfd109312eb,

title = "On the Depth of Modular Invariant Rings for the Groups C p × C p",

abstract = "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 R G is at least min{ dim(V ), dim(VP )+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 Cp ×Cp, generating many new examples of flat modules. We introduce the useful notion of “strongly flat” modules, classifying 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.",

keywords = "modular invariant theory, modular representation theory, depth, transfer , cohomology",

author = "Jonathan Elmer and Peter Fleischmann",

year = "2009",

doi = "10.1007/978-0-8176-4875-6_4",

language = "English",

isbn = "978-0-8176-4874-9",

series = "Progress in Mathematics",

publisher = "Springer ",

pages = "45--61",

editor = "Campbell, {H E A} and Helminck, {Aloysius G} and Hanspeter Kraft and David Wehalu",

booktitle = "Symmetry and Spaces",

}