On an extremal property of Jordan algebras of Clifford type

Abstract

If $V$ is a finite-dimensional unital commutative (maybe nonassociative) algebra carrying an associative positive definite bilinear form then there exist a nonzero idempotent $c\ne e$ ($e$ being the algebra unit) of the shortest possible length $|c{|}^2$. In particular, $|c{|}^2\le \frac{1}{2}|e{|}^2$. We prove that the equality holds exactly when $V$ is a Jordan algebra of Clifford type.

arXiv comment9 pages, submitted