Super Jordan triple systems and Kantor triple systems

We introduce the notion of $ \epsilon $-super Jordan triple systems(sJTS), a supersymmetric generalization of Jordan triple systems which includes them as well as the class of N=6 3-algebras as particular cases. The Tits-Kantor-Koecher construction for Kantor triple systems(KTS) and for $ \epsilon $-super Jordan triple systems is established and thanks to it the problem of classifying simple linearly-compact KTS and sJTS is reduced to the classification of particular classes of automorphisms of 5-graded Lie algebras and 3-graded Lie superalgebras. We obtain the classification of simple linearly-compact KTS and the classification of finite-dimensional simple sJTS.