Integrality over fixed rings of automorphisms in a Lie nilpotent setting]

JOURNAL OF ALGEBRA

卷:518

Article

Szigeti, Jeno¹ 

[1] Univ Miskolc, Inst Math, H-3515 Miskolc, Hungary

关键词: Lie nilpotent algebra;    Fixed ring of automorphisms;    Skew polynomial algebra;   

DOI  :  10.1016/j.jalgebra.2018.10.009

来源: Elsevier

【 摘 要 】

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 subset of 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 delta is an element of K, for a K-automorphism is an element of Aut(K)(R) with delta(n) = id(R), we prove that the skew polynomial algebra R[omega, delta] is right integral of degree nk over Fix(delta) [omega(n)]. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free