A Characterization of (−1, −1)-Freudenthal–kantor Triple Systems

Abstract

Abstract. In this paper, we discuss a connection between (−1, −1)-FreudenthalKantor triple systems, anti-structurable algebras, quasi anti-flexible algebras and give examples of such structures. The paper provides the correspondence and characterization of a bilinear product corresponding a triple product. associated with an (ε, δ)-Freudenthal-Kantor triple system. In particular, we deal with a characterization of triple systems from the point of view of a bilinear product by means of anti-structurable algebras or balanced property. Specially, Jordan and Lie (super)algebras [9, 13, 52] play an important role in many mathematical and physical subjects [ 5, 11-14, 16, 26, 29, 37, 47, 48, 55, 56]). We also note that the construction and characterization of these algebras can be expressed in terms of triple systems [20, 23,24,28,38,49] by using the standard embedding method [22,41,42,50,54].