Gradings on associative triple systems of the second kind

Abstract

On this work we study associative triple systems of the second kind. We show that for simple triple systems the automorphism group scheme is isomorphic to the automorphism group scheme of the $3$-graded associative algebra with involution constructed by Loos. This result will allow us to prove our main result which is a complete classification up to isomorphism of the gradings of structurable algebras.