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Klein four-subgroups
of Lie algebra automorphisms
Jing-Song Huang and Jun Yu |
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Vol. 262 (2013), No. 2, 397–420
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Abstract |
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We classify the Klein four-subgroups Γ of Aut(u0) for each compact simple Lie algebra u0 up to conjugation, by calculating the symmetric subgroups Aut(u0)𝜃 and their involution classes. This leads to a new approach to the classification of semisimple symmetric pairs and ℤ2 × ℤ2-symmetric spaces. We also determine the fixed point subgroups Aut(u0)Γ. |
Keywords
automorphism group, involution, symmetric subgroup, Klein
four-group, involution type
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Mathematical Subject Classification 2010
Primary: 20E45
Secondary: 53C35
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Milestones
Received: 17 January 2012
Revised: 15 July 2012
Accepted: 20 August 2012
Published: 16 April 2013
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Authors |
| Jing-Song Huang | |
| Department of Mathematics Hong Kong University of Science and Technology (HKUST) Kowloon Hong Kong SAR China |
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| Jun Yu | |
| Department of Mathematics ETH Zurich 8092 Zurich Switzerland |
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