Locally finite derivations and modular coinvariants

2016/05/20 by Elmer, Jonathan, Sezer, Mufit · 1 citation
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.06363

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, \citeSezerCoinv. 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 \citeSezerShank.

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• Homological properties of invariant rings of permutation groups

Related

• Coinvariants for modular representations of cyclic groups of prime order
• Cohen-Macaulay modules of covariants for cyclic p-groups
• Modular Covariants of Cyclic Groups of Order p
• Higher Specht bases for generalizations of the coinvariant ring
• On Hilbert ideals for a class of p-groups in characteristic p