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arXiv · 1801.05724

On an extremal property of Jordan algebras of Clifford type

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

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Vladimir G. Tkachev. 2018-01-17. On an extremal property of Jordan algebras of Clifford type. https://arxiv.org/abs/1801.05724

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