Klein Four subgroups of Lie Algebra Automorphisms

2011/08/10 by Jing-Song Huang, Jun Yu, Huang, Jing-Song +1 · 1 citation
Mathematics · #17B40 #22E15 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1108.2397

openalex publication_date 2011/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By calculating the symmetric subgroups \Aut(\fru₀)^θ and their involution classes, we classify the Klein four subgroups Γ of \Aut(\fru₀) for each compact simple Lie algebra \fru₀ up to conjugation. This leads to a new approach of classification of semisimple symmetric pairs and \bbZ₂× \bbZ₂-symmetric spaces. We also determine the fixed point subgroup \Aut(\fru₀)^Γ.

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• Elementary abelian 2 subgroups of compact Lie groups

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