Jordan superalgebras defined by brackets

摘要

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