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arXiv · 1501.07104

Integrality over fixed rings of automorphisms in a Lie nilpotent setting

Jeno Szigeti
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Abstract

Let R be a Lie nilpotent algebra of index k over a field K of characteristic zero. If G is an n-element subgroup of Aut(R) of the 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 in K, for a K-automorphism d in Aut(R) with d^n=id, we prove that the skew polynomial algebra R[w,d] is right integral of degree n^k over Fix(d)[w^n].

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Jeno Szigeti. 2018-12-26. Integrality over fixed rings of automorphisms in a Lie nilpotent setting. https://arxiv.org/abs/1501.07104

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