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 ≠ e (e being the algebra unit) of the shortest possible length . In particular, there always holds . We prove that the equality for some idempotent c ∈ V holds exactly when V is a Jordan algebra of Clifford type.
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