Klein Four subgroups of Lie Algebra Automorphisms

Details Klein Four subgroups of Lie Algebra Automorphisms Klein Four subgroups of Lie Algebra Automorphisms

2011-08-10

arxiv.org/abs/1108.2397v1

Mathematics

Group Theory

19 pages

Scientific paper

By calculating the symmetric subgroups $\Aut(\fru_0)^{\theta}$ and their involution classes, we classify the Klein four subgroups $\Gamma$ of $\Aut(\fru_0)$ for each compact simple Lie algebra $\fru_0$ up to conjugation. This leads to a new approach of classification of semisimple symmetric pairs and $\bbZ_2\times \bbZ_2$-symmetric spaces. We also determine the fixed point subgroup $\Aut(\fru_0)^\Gamma$.

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