Depth and detection in modular invariant theory

Article


Elmer, J. 2009. Depth and detection in modular invariant theory. Journal of Algebra. 322 (5), pp. 1653-1666. https://doi.org/10.1016/j.jalgebra.2009.04.036
TypeArticle
TitleDepth and detection in modular invariant theory
AuthorsElmer, J.
Abstract

Let G be a finite group acting linearly on a vector space V over a field of characteristic p dividing the group order, and let R denote S(V∗). We study the R^G modules H^i(G, R), for i ≥ 0 with R^G itself as a special case. There are lower bounds for depth of (H^i(G, R)) and for depth(R^G). We show that a certain sufficient condition for their attainment (due to Fleischmann, Kemper and Shank) may be modified to give a condition which is both necessary and sufficient. We apply our main result to classify the representations of the Klein four-group for which depth(R^G) attains its lower bound. We also use our new condition to show that the if G = P × Q, with P a p-group and Q an abelian p'-group, then the depth of R G attains its lower bound if and only if the depth of R^P does so.

LanguageEnglish
PublisherElsevier
JournalJournal of Algebra
ISSN0021-8693
Publication dates
Print01 Sep 2009
Publication process dates
Deposited14 Apr 2016
Accepted24 Apr 2009
Output statusPublished
Additional information

Available online 12 May 2009

Digital Object Identifier (DOI)https://doi.org/10.1016/j.jalgebra.2009.04.036
First submitted version
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https://repository.mdx.ac.uk/item/863v6

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