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Transactions of the American Mathematical Society

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

 

 

Noncommutative Jordan algebras of capacity two


Author: Kirby C. Smith
Journal: Trans. Amer. Math. Soc. 158 (1971), 151-159
MSC: Primary 17.40
DOI: https://doi.org/10.1090/S0002-9947-1971-0277584-6
MathSciNet review: 0277584
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Abstract: Let $ J$ be a noncommutative Jordan algebra with 1. If $ J$ has two orthogonal idempotents $ e$ and $ f$ such that $ 1 = e + f$ and such that the Peirce $ 1$-spaces of each are Jordan division rings, then $ J$ is said to have capacity two. We prove that a simple noncommutative Jordan algebra of capacity two is either a Jordan matrix algebra, a quasi-associative algebra, or a type of quadratic algebra whose plus algebra is a Jordan algebra determined by a nondegenerate symmetric bilinear form.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0277584-6
Keywords: Simple noncommutative Jordan algebra, capacity two, quasi-associative algebra
Article copyright: © Copyright 1971 American Mathematical Society