The Tits—kantor—koecher Construction for Jordan Dialgebras
نویسنده
چکیده
We study a noncommutative generalization of Jordan algebras called Leibniz— Jordan algebras. These algebras satisfy the identities [x1x2]x3 = 0, (x 2 1 , x2, x3) = 2(x1, x2, x1x3), x1(x 2 1 x2) = x 2 1 (x1x2); they are related with Jordan algebras in the same way as Leibniz algebras are related to Lie algebras. We present an analogue of the Tits— Kantor—Koecher construction for Leibniz—Jordan algebras that provides an embedding of such an algebra into Leibniz algebra.
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