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A Note on Triple Systems and Totally Geodesic Submanifolds in a Homogeneous Space

Published online by Cambridge University Press:  22 January 2016

Arthur A. Sagle
Arthur A. Sagle*
Affiliation:
University of Minnesota
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In the study of nonassociative algebras various “triple systems” frequently arise from the associator function and other multilinear objects. In particular Lie triple systems arise in the study of Jordan algebras and a generalization of a Lie triple system arises in Malcev algebras. Lie triple systems also are used to study totally geodesic submanifolds of a Riemannian symmetric space. We shall show how a generalization of Lie triple systems also arises from the study of curvature and geodesies of a torsion free connexion on a manifold and bring out the relation of this to various nonassociative algebras.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 32 , June 1968 , pp. 5 - 20
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

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