Double automorphisms of graded Lie algebras

JOURNAL OF ALGEBRA

卷:387

Article

Acciarri, Cristina¹  Shumyatsky, Pavel¹ 

[1] Univ Brasilia, Dept Math, BR-70910900 Brasilia, DF, Brazil

关键词: Automorphisms;    Graded Lie algebras;   

DOI  :  10.1016/j.jalgebra.2012.12.023

来源: Elsevier

【 摘 要 】

We introduce the concept of a double automorphism of an A-graded Lie algebra L. Roughly, this is an automorphism of L which also induces an automorphism of the group A. It is clear that the set of all double automorphisms of L forms a subgroup in Aut L. In the present paper we prove several nilpotency criteria for a graded Lie algebra admitting a finite group of double automorphisms. One of the obtained results is as follows. Let A be a torsion-free abelian group and L an A-graded Lie algebra in which [L, L-0,L- ... , L-0] = 0. Assume that L admits a finite group of double automorphisms H such that C-A(h) = 0 for all non-trivial h is an element of H and C-L(H) is nilpotent of class c. Then L is nilpotent and the class of L is bounded in terms of vertical bar H vertical bar, k and c only. We also give an application of our results to groups admitting a Frobenius group of automorphisms. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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