Jordan superalgebras defined by brackets

Jordan superalgebras defined by brackets on associative commutative superalgebras are studied. It is proved that any such a superalgebra is imbedded into a superalgebra defined by Poisson brackets. In particular, all Jordan superalgebras of brackets are i-special. The speciality of these superalgebras is also examined, and it is proved, in particular, that the Cheng-Kac superalgebra is special.

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C. Martinez <chelo@pinon.ccu.uniovi.es> I. Shestakov <shestak@ime.usp.br> E. Zelmanov <zelmanov@PASCAL.MATH.YALE.EDU>