On an extremal property of Jordan algebras of Clifford type

17 Jan 2018  ·  Tkachev Vladimir G. ·

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, $|c|^2\le \frac12|e|^2$... We prove that the equality holds exactly when $V$ is a Jordan algebra of Clifford type. read more

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Rings and Algebras Commutative Algebra