Klein Four subgroups of Lie Algebra Automorphisms
Jing-Song Huang, Jun Yu

TL;DR
This paper classifies Klein four subgroups within automorphism groups of compact simple Lie algebras, providing a new method for classifying symmetric pairs and spaces with specific involution structures.
Contribution
It introduces a systematic classification of Klein four subgroups in Lie algebra automorphisms, enhancing understanding of symmetric pairs and spaces.
Findings
Classification of Klein four subgroups up to conjugation
Determination of fixed point subgroups for these Klein four subgroups
A new approach to classifying semisimple symmetric pairs
Abstract
By calculating the symmetric subgroups and their involution classes, we classify the Klein four subgroups of for each compact simple Lie algebra up to conjugation. This leads to a new approach of classification of semisimple symmetric pairs and -symmetric spaces. We also determine the fixed point subgroup .
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology
