5-Graded Lie Superalgebras and Jordan-Kantor Superpairs

We introduce the notions of a Kantor superpair and a Jordan-Kantor superpair, by using which we construct 5-graded Lie superalgebras. In addition, the relationship between a Jordan-Kantor superpair [Formula: see text] and the corresponding 5-graded Lie superalgebra [Formula: see text] is described. We also characterize the universal central extension of the 5-graded Lie superalgebra [Formula: see text] with [Formula: see text] being the inner structure superalgebra of [Formula: see text]. Finally, we obtain a realization of a class of 5-graded Lie superalgebras, termed 5-graded Lie superalgebras of type [Formula: see text], with the aid of Jordan-Kantor superpairs.