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Erschienen in:
2017 | OriginalPaper | Buchkapitel
Maximal Antipodal Subgroups of the Automorphism Groups of Compact Lie Algebras
verfasst von : Makiko Sumi Tanaka, Hiroyuki Tasaki
Erschienen in: Hermitian–Grassmannian Submanifolds
Verlag: Springer Singapore
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Abstract
We classify maximal antipodal subgroups of the group \(\mathrm {Aut}(\mathfrak {g})\) of automorphisms of a compact classical Lie algebra \(\mathfrak {g}\). A maximal antipodal subgroup of \(\mathrm {Aut}(\mathfrak {g})\) gives us as many mutually commutative involutions of \(\mathfrak {g}\) as possible. For the classification we use our former results of the classification of maximal antipodal subgroups of quotient groups of compact classical Lie groups. We also use canonical forms of elements in a compact Lie group which is not connected.