On constructions of Lie (super) algebras and (𝜀,δ)-Freudenthal–Kantor triple systems defined by bilinear forms

Abstract

In this work, we discuss a classification of [Formula: see text]-Freudenthal–Kantor triple systems defined by bilinear forms and give all examples of such triple systems. From these results, we may see a construction of some simple Lie algebras or superalgebras associated with their Freudenthal–Kantor triple systems. We also show that we can associate a complex structure into these ([Formula: see text]-Freudenthal–Kantor triple systems. Further, we introduce the concept of Dynkin diagrams associated to such [Formula: see text]-Freudenthal–Kantor triple systems and the corresponding Lie (super) algebra construction.

On the Faulkner construction for generalized Jordan superpairs

“…Some constructions of Lie algebras from ternary algebras appear in [A76], [F71]. Kantor pairs are also called generalized Jordan pairs of second order (see [KM20] and references therein). For the basic definitions related to Lie superalgebras see, e.g., [CW12], [K77].…”