3 Review(s)

We classify graded simple Jordan superalgebras of growth one which correspond the so called 'superconformal algebras' via the Tits-Kantor-Koecher construction. The superconformal algebras with a 'hidden' Jordan structure are those of type $K$ and the recently discovered Cheng-Kac superalgebras $CK(6)$. We show that Jordan superalgebras related to the type $K$ are Kantor Doubles of some Jordan brackets on associative commutative superalgebras and list these brackets.