On graded Lie algebras of characteristic three with classical reductive null component

JOURNAL OF ALGEBRA

卷:538

Article

Gregory, T. B.¹  Kuznetsov, M., I² 

[1] Ohio State Univ, Dept Math, Mansfield, OH 44906 USA

[2] Nizhnii Novgorod State Univ, Dept Math, Nizhnii Novgorod 603600, Russia

关键词: Lie algebras;    Graded Lie algebras;    Prime-characteristic Lie algebras;   

DOI  :  10.1016/j.jalgebra.2019.06.035

来源: Elsevier

【 摘 要 】

We consider finite-dimensional irreducible transitive graded Lie algebras L = Sigma(r)(i=-q) L-i over algebraically closed fields of characteristic three. We assume that the null component L-0 is classical and reductive. The adjoint representation of L on itself induces a representation of the commutator subalgebra L-0' of the null component on the minus-one component L-1. We show that if the depth q and height r of L are both greater than one, then this representation must be restricted. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free