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Transactions of the American Mathematical Society

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

 

 

Representations of Jordan triples


Author: Ottmar Loos
Journal: Trans. Amer. Math. Soc. 185 (1973), 199-211
MSC: Primary 17C15
DOI: https://doi.org/10.1090/S0002-9947-1973-0327857-5
MathSciNet review: 0327857
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Abstract: Some standard results on representations of quadratic Jordan algebras are extended to Jordan triples. It is shown that the universal envelope of a finite-dimensional Jordan triple is finite-dimensional, and that it is nilpotent if the Jordan triple is radical. A permanence principle and a duality principle are proved which are useful in deriving identities.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0327857-5
Keywords: Jordan triple, Jordan algebra, representation, universal envelope, nilpotence
Article copyright: © Copyright 1973 American Mathematical Society