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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Jordan algebras and connections on homogeneous spaces

Author: Arthur A. Sagle
Journal: Trans. Amer. Math. Soc. 187 (1974), 405-427
MSC: Primary 53C30
MathSciNet review: 0339013
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Abstract: We use the correspondence between G-invariant connections on a reductive homogeneous space $ G/H$ and certain nonassociative algebras to explicitly compute the pseudo-Riemannian connections in terms of a Jordan algebra J of endomorphisms. It is shown that if G and H are semisimple Lie groups, then J is a semisimple Jordan algebra. Also a general method for computing examples of J is given.

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Keywords: Reductive pair, homogeneous space, pseudo-Riemannian connection, nonassociative algebra, Jordan algebra, Taylor series
Article copyright: © Copyright 1974 American Mathematical Society

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