Graded polynomial identities, group actions, and exponential growth of Lie algebras

JOURNAL OF ALGEBRA

卷:367

Article

Gordienko, A. S.

关键词: Lie algebra;    Polynomial identity;    Grading;    Codimension;    Cocharacter;    Symmetric group;    Young diagram;    Group action;   

DOI  :  10.1016/j.jalgebra.2012.05.021

来源: Elsevier

【 摘 要 】

Consider a finite dimensional Lie algebra L with an action of a finite group G over a field of characteristic O. We prove the analog of Amitsur's conjecture on asymptotic behavior for codimensions of polynomial G-identities of L. As a consequence, we prove the analog of Amitsur's conjecture for graded codimensions of any finite dimensional Lie algebra graded by a finite Abelian group. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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