Abstract:Let J 1 and J 2 be two Jordan algebras with unit elements. We define various tensor products of J 1 and J 2 . The first, which we call the Kronecker product, is the most obvious and is based on the te...Let J 1 and J 2 be two Jordan algebras with unit elements. We define various tensor products of J 1 and J 2 . The first, which we call the Kronecker product, is the most obvious and is based on the tensor product of the vector spaces. We find conditions sufficient for its existence and for its non-existence. Motivated by the universal mapping property for the tensor product of associative algebras we define, in Section 2, tensor products of J 1 and J 2 by means of a universal mapping property. The tensor products always exist for special Jordan algebras and need not coincide with the Kronecker product when the latter exists. In Section 3 we construct a more concrete tensor product for special Jordan algebras. Here the tensor product of a special Jordan algebra and an associative Jordan algebra coincides with the Kronecker product of these algebras. We show that this "special" tensor product is the natural tensor product for some Jordan matrix algebras.Read More