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Noncommutative duplicate and Jordan algebras. II. (English) Zbl 1266.17019
Summary: Let $$K$$ be a commutative field of characteristic zero. Let $$A$$ be a finite dimensional algebra over $$K$$, not necessarily commutative and $$D(A)$$ the noncommutative duplicate of $$A$$. Here we give necessary and sufficient conditions for $$D(A)$$ to be a Jordan algebra.
For part I, see [the first author, Adv. Theor. Appl. Math. 5, No. 2, 223–235 (2010)].
##### MSC:
 17C99 Jordan algebras (algebras, triples and pairs)