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Maximal Antipodal Subgroups of the Automorphism Groups of Compact Lie Algebras

  • Makiko Sumi TanakaEmail author
  • Hiroyuki Tasaki
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 203)

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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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Faculty of Science and Technology, Department of MathematicsTokyo University of ScienceNodaJapan
  2. 2.Faculty of Pure and Applied Sciences, Division of MathematicsUniversity of TsukubaTsukubaJapan

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