Jordan superalgebras defined by brackets
Consuelo Martínez, Ivan Shestakov, and Efim Zelmanov
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.