ABSTRACT
In his classification theorem, V.G. Kac used the corresponding result for Lie superalgebras and the relations between Jordan and Lie structures. M. Racine and E. Zelmanov obtained a classification of simple Jordan superalgebras over fields of characteristic p is not equal to 2 whose even part is semisimple. This chapter pays special attention to finite dimensional modular Jordan superalgebras whose even part is not semisimple. A superconformai algebra is a Z-graded simple Lie superalgebra that contains the Virasoro algebra in the even part and such that dimensions of all the homogeneous components, dimLi, are uniformely bounded. The Tits-Kantor-Koecher construction establish connections between Lie algebras (resp. Lie superalgebras) and Jordan algebras (resp. Jordan superalgebras).
