Derivations of the Cheng–Kac Jordan superalgebras

The derivations of the Cheng–Kac Jordan superalgebras are studied. It is shown that, assuming −1 is a square in the ground field, the Lie superalgebra of derivations of a Cheng–Kac Jordan superalgebra is isomorphic to the Lie superalgebra obtained from a simpler Jordan superalgebra (a Kantor double superalgebra of vector type) by means of the Tits–Kantor–Koecher construction. This is done by exploiting the S4-symmetry of the Cheng–Kac Jordan superalgebra.