Locally finite derivations and modular coinvariants

Jonathan Elmer, Müfit Sezer (Corresponding Author)

Research output: Contribution to journalArticle

Abstract

We consider a finite dimensional $\kk G$-module V of a p-group G over a field $\kk$ of characteristic p. We describe a generating set for the corresponding Hilbert Ideal. In case G is cyclic this yields that the algebra $\kk[V]_G$ of coinvariants is a free module over its subalgebra generated by $\kk G$-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, \cite{SezerCoinv}. 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 \cite{SezerShank}.
Original languageEnglish
Pages (from-to)1053-1062
Number of pages10
JournalQuarterly Journal of Mathematics
Volume69
Issue number3
Early online date16 Mar 2018
DOIs
Publication statusPublished - 30 Sep 2018

Fingerprint

Module
Hilbert
Subalgebra
Generating Set
Complete Intersection
Polynomial ring
P-groups
Quotient
Isomorphic
Generator
Ring
Algebra

Keywords

  • Invariant theory
  • coinvariants
  • prime characteristic

Cite this

Locally finite derivations and modular coinvariants. / Elmer, Jonathan; Sezer, Müfit (Corresponding Author).

In: Quarterly Journal of Mathematics, Vol. 69, No. 3, 30.09.2018, p. 1053-1062.

Research output: Contribution to journalArticle

Elmer, Jonathan ; Sezer, Müfit. / Locally finite derivations and modular coinvariants. In: Quarterly Journal of Mathematics. 2018 ; Vol. 69, No. 3. pp. 1053-1062.
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