Remote Access Transactions of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9947-1974-0339013-6
MathSciNet review: 0339013
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 53C30

Retrieve articles in all journals with MSC: 53C30


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0339013-6
Keywords: Reductive pair, homogeneous space, pseudo-Riemannian connection, nonassociative algebra, Jordan algebra, Taylor series
Article copyright: © Copyright 1974 American Mathematical Society