Kantor triple systems and supersymmetric Jordan triple systems

In this seminar we will talk about two generalizations of Jordan triple systems: the triple systems originally introduced by I. L. Kantor in the 1970s and the contemporary supersymmetric Jordan triple systems. We will describe their relation with graded Lie (super)algebras with involutions via the TKK construction and discuss their classification. Explicit examples will be given, both in the finite-dimensional and infinite-dimensional case.