Integrality over fixed rings of automorphisms in a Lie nilpotent setting

Abstract

Let R be a Lie nilpotent algebra of index k≥1 over a field K of characteristic zero. If G is an n-element subgroup G⊆AutK(R) of K-automorphisms, then we prove that R is right integral over Fix(G) of degree nk. In the presence of a primitive n-th root of unity e∈K, for a K-automorphism δ∈AutK(R) with δn=idR, we prove that the skew polynomial algebra R[w,δ] is right integral of degree nk over Fix(δ)[wn].