Locally finite derivations and modular coinvariants

Article


Elmer, J. and Sezer, M. 2018. Locally finite derivations and modular coinvariants. Quarterly Journal of Mathematics. 69 (3), pp. 1053-1062. https://doi.org/10.1093/qmath/hay013
TypeArticle
TitleLocally finite derivations and modular coinvariants
AuthorsElmer, J. and Sezer, M.
Abstract

We consider a finite dimensional kG-module V of a p-group G over a field k of characteristic p. We describe a generating set for the corresponding Hilbert Ideal. In case G is cyclic this yields that the algebra k[V]_G of coinvari-ants is a free module over its subalgebra generated by kG-module generators of V^∗ . This subalgebra is a quotient of a polynomial ring by pure powers of its variables. The coinvariant ring was known to have this property only when G was cyclic of prime order. In addition, we show that if G is the Klein 4-group and V does not contain an indecomposable summand isomorphic to the regular module, then the Hilbert Ideal is a complete intersection, extending a result of the second author and R. J. Shank.

LanguageEnglish
PublisherOxford University Press (OUP)
JournalQuarterly Journal of Mathematics
ISSN0033-5606
Publication dates
Online16 Mar 2018
Print01 Sep 2018
Publication process dates
Deposited20 Feb 2018
Accepted14 Feb 2018
Output statusPublished
Accepted author manuscript
Copyright Statement

This is a pre-copyedited, author-produced version of an article accepted for publication in Quarterly Journal of Mathematics following peer review. The version of record, Jonathan Elmer, Müfit Sezer, Locally finite derivations and modular coinvariants, The Quarterly Journal of Mathematics, Volume 69, Issue 3, September 2018, Pages 1053–1062, , is available online at: https://academic.oup.com/qjmath/article/69/3/1053/4938528 and
https://doi.org/10.1093/qmath/hay013

Digital Object Identifier (DOI)https://doi.org/10.1093/qmath/hay013
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