Lie algebras simple with respect to a Taft algebra action

JOURNAL OF ALGEBRA

卷:517

Article

Gordienko, Alexey¹ 

[1] Vrije Univ Brussel, Brussels, Belgium

关键词: Polynomial identity;    H-module algebra;    Taft algebra;    Codimension;    PI-exponent;    Lie algebra;   

DOI  :  10.1016/j.jalgebra.2018.10.008

来源: Elsevier

【 摘 要 】

We classify finite dimensional H-m2(zeta)-simple H-m2 (zeta)-module Lie algebras L over an algebraically closed field of characteristic 0 where H-m2(zeta) is the mth Taft algebra. As an application, we show that despite the fact that L can be non-semisimple in ordinary sense, lim(n)->infinity (n)root c(n)(Hm2(zeta))(L) = dim L where c(n)(Hm2(zeta))(L) is the codimension sequence of polynomial H-m2(zeta)-identities of L. In particular, the analog of Amitsur's conjecture holds for c(n)(Hm2(zeta))(L). (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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