Higher order symmetric spaces and the roots of the identity in a Lie group |
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Authors: | Cecí lia Ferreira Armando Machado |
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Affiliation: | CMAF da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal ; CMAF da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal |
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Abstract: | Let denote the set of all -roots of the identity in a Lie group . We show that is always an embedded submanifold of , having the conjugacy classes of its elements as open submanifolds. These conjugacy classes are examples of -symmetric spaces and we show, more generally, that every -symmetric space of a Lie group is a covering manifold of an embedded submanifold of . We compute also the Hessian of the inclusions of and into , relative to the natural connection on the domain and to the symmetric connection on . |
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Keywords: | Lie group orbit $k$-symmetric space $k$-root of the identity. |
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