ABSTRACT
The concept of the standard embedding plays an important role in the theory of a construction of Lie algebras from triple systems, in particular, Frudenthal-Kantor triple systems and Lie triple systems are intimately related to Lie algebras as well as Lie superalgebras. It is interesting to study how the standard embedding behaves for Jordan-Lie triple systems with familiar connection to Jordan superalgebras. The aim is to give an unified explicit frame work for the construction of simple Jordan superalgebras and is to characterize it by concept of our triple systems. This chapter deals with algebra and triple systems which are finite dimensional over a field Φ of characteristic≠2. It gives several examples of simple Jordan superalgebras. The chapter describes a characterization of the definition of Jordan superalgebras due to V.G. Kac.
