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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Koecher's principle for quadratic Jordan algebras


Author: Kevin McCrimmon
Journal: Proc. Amer. Math. Soc. 28 (1971), 39-43
MSC: Primary 17C05
MathSciNet review: 0299649
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Abstract: In this note we indicate two techniques for establishing identities in quadratic Jordan algebras. The first method, due to Professor M. Koecher, shows that to establish an identity in general it suffices to establish it when all the elements involved are invertible. The second technique involves interpreting a given identity in a Jordan algebra as a simpler identity in a homotope of that algebra. These two techniques are applied to derive some important identities.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0299649-0
PII: S 0002-9939(1971)0299649-0
Keywords: Quadratic Jordan algebras, identities
Article copyright: © Copyright 1971 American Mathematical Society