Triality groups associated with triple systems and their homotope algebras
Abstract
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.
Keywords
(α,β,γ) triple systems; Freudenthal-Kantor triple systems; triality relations; generalization of automorphisms and derivations
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Research Institute for Mathematical Algebras Sciences (RIMAS), Chigasaki City, Japan Japan
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