The Tits--Kantor--Koecher construction for Jordan dialgebras

Details The Tits--Kantor--Koecher construction for Jordan dialgebras The Tits--Kantor--Koecher construction for Jordan dialgebras

2009-07-10

arxiv.org/abs/0907.1740v3

Comm. Algebra 39 (2011) no. 2, 497--520

Mathematics

Rings and Algebras

22 pages; v2: Example 4 corrected; v3: final version, to appear in Comm. Algebra

Scientific paper

We study a noncommutative generalization of Jordan algebras called Jordan dialgebras. These are algebras that satisfy the identities $[x_1 x_2]x_3= 0$, $(x_1^2,x_2,x_3)=2(x_1,x_2,x_1x_3)$, $x_1(x_1^2 x_2)=x_1^2(x_1 x_2)$; 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 Jordan dialgebras that provides an embedding of such an algebra into Leibniz algebra.

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