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 ⊆ Aut K ( R ) of K -automorphisms, then we prove that R is right integral over Fix ( G ) of degree n k . In the presence of a primitive n -th root of unity e ∈ K , for a K -automorphism δ ∈ Aut K ( R ) with δ n = id R , we prove that the skew polynomial algebra R [ w , δ ] is right integral of degree n k over Fix ( δ ) [ w n ] .