Computing Chevalley bases in small characteristics

JOURNAL OF ALGEBRA

卷:322

Article

Cohen, Arjeh M.¹  Roozemond, Dan¹ 

[1] Tech Univ Eindhoven, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands

关键词: Lie algebras;    Chevalley bases;    Conjugacy problems;    Isomorphism problems;    Total subalgebras;    Algorithms;    Groups of Lie type;   

DOI  :  10.1016/j.jalgebra.2009.04.038

来源: Elsevier

【 摘 要 】

Let L be the Lie algebra of a simple algebraic group defined over a field F and let H be a split maximal total subalgebra of L. Then L has a Chevalley basis with respect to H. If char(F) not equal 2, 3, it is known how to find it. In this paper, we treat the remaining two characteristics. To this end, we present a few new methods, implemented in MAGMA, which vary from the computation of centralizers of one root space in another to the computation of a specific part of the Lie algebra of derivations of L. (C) 2009 Elsevier Inc, All rights reserved.

【 授权许可】

Free