Maximal abelian subgroups of compact simple Lie groups

2012/10/31 by Jun Yu, Yu, Jun · 4 citations
Mathematics · #20E07 #20E45 #20K27 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Geometry and complex manifolds #Group Theory (math.GR) #math.GR #msc:20E07 #msc:20E45 #msc:20K27

paper · pdf · doi:10.48550/arxiv.1211.1334

Replaced by arXiv:1403.2680

openalex publication_date 2012/10/31 · arxiv created 2021/02/05 · arxiv updated 2021/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify abelian subgroups of the automorphism group of any compact simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup. This leads to a classification of the maximal abelian subgroups of compact simple groups of adjoint type and a classification of the fine group gradings of complex simple Lie algebras.

Citations

• Elementary abelian p-subgroups of algebraic groups
• Fine gradings on simple classical Lie algebras
• Maximal abelian subgroups of compact simple Lie groups of type E

Cited by

• Weyl groups of the fine gradings on \e₆
• Maximal abelian subgroups of compact matrix groups
• Maximal abelian subgroups of Spin groups and some exceptional simple Lie groups
• Maximal abelian subgroups of compact simple Lie groups of type E

Related

• Maximal abelian subgroups of compact matrix groups
• Maximal abelian subgroups of compact simple Lie groups of type E
• Maximal abelian subgroups of Spin groups and some exceptional simple Lie groups
• Elementary abelian 2 subgroups of compact Lie groups
• Exceptional Lie groups