JORDAN SUPERALGEBRAS DEFINED BY BRACKETS

CONSUELO MARTÍNEZ IVAN SHESTAKOV EFIM ZELMANOV

Abstract. 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.