Hermitian–Grassmannian Submanifolds pp 39-47 | Cite as
Maximal Antipodal Subgroups of the Automorphism Groups of Compact Lie Algebras
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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.
Notes
Acknowledgements
The authors would like to thank Osamu Ikawa for his providing information about Proposition 3. The first author was partly supported by the Grant-in-Aid for Science Research (C) (No. 15K04855), Japan Society for the Promotion of Science. The second author was partly supported by the Grant-in-Aid for Science Research (C) (No. 15K04835), Japan Society for the Promotion of Science.
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