Triality groups associated with triple systems and their homotope algebras - Kamiya, Noriaki (Annales Mathematicae Silesianae, 2021)
We introduce the notion of an (α,β,γ) triple system, which generalizes the familiar generalized Jordan triple system related to a construction of simple Lie algebras. We then discuss its realization by considering some bilinear algebras and vice versa. Next, as a new concept, we study triality relations (a triality group and a triality derivation) associated with these triple systems; the relations are a generalization of the automorphisms and derivations of the triple systems. Also, we provide examples of several involutive triple systems with a tripotent element.