Locally finite derivations and modular coinvariants

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.

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