The isomorphism type of the centralizer of an element in a Lie group

JOURNAL OF ALGEBRA

卷:376

Article

Duan, Haibao¹  Liu, Shali¹ 

[1] Chinese Acad Sci, Inst Math, Hua Loo Keng Key Lab Math, Beijing 100864, Peoples R China

关键词: Lie groups;    Centralizer;    Homogeneous spaces;   

DOI  :  10.1016/j.jalgebra.2012.10.028

来源: Elsevier

【 摘 要 】

Let G be a compact 1-connected simple Lie group, and let x is an element of G be a group element. We determine the isomorphism type of the centralizer C-x in term of a minimal geodesic joining the group unit e is an element of G to x. This result is applied to classify the isomorphism types of maximal subgroups of maximal rank of G (Borel and De Siebenthal, 1949 [4]), and the isomorphism types of parabolic subgroups of G. (c) 2012 Elsevier Inc. All rights reserved.

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