Noncommutative Jordan algebras of capacity two

Smith, Kirby C.

doi:10.1090/S0002-9947-1971-0277584-6

Noncommutative Jordan algebras of capacity two
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by Kirby C. Smith PDF

Trans. Amer. Math. Soc. 158 (1971), 151-159 Request permission

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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