Jordan algebras and connections on homogeneous spaces

Sagle, Arthur A.

doi:10.1090/S0002-9947-1974-0339013-6

Jordan algebras and connections on homogeneous spaces
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by Arthur A. Sagle PDF

Trans. Amer. Math. Soc. 187 (1974), 405-427 Request permission

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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