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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Clifford translations of symmetric spaces


Author: V. Ozols
Journal: Proc. Amer. Math. Soc. 44 (1974), 169-175
MSC: Primary 53C35
DOI: https://doi.org/10.1090/S0002-9939-1974-0334093-1
MathSciNet review: 0334093
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Abstract: A direct proof, not using the classification of symmetric spaces, is given for the following characterization of Clifford translations in a symmetric space $ M$: An isometry $ g$ is a Clifford translation of $ M$ if and only if the centralizer $ Z(g)$ of $ g$ in the isometry group of $ M$ is transitive on $ M$. The proof uses a geodesic characterization of Clifford translations, and the subgroups $ {T^{(h)}}$ of J. de Siebenthal.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0334093-1
Keywords: Clifford translation, isometry, symmetric space, homogeneous space
Article copyright: © Copyright 1974 American Mathematical Society