Some Properties Of Jordan Lie Superalgebra

As a natural generalization of Jordan Lie algebras and Lie superalgebras, Jordan Lie superalgebras and its properties were first given by S.Okubo and N.Kamiya in 1997 [1]. By now, the study on Jordan Lie superalgebras is few[2]. In this thesis, I first introduce the definitions of ideals and quotient algebras, and give their some elementary properties, respectively. I then prove that some theorems of homomorphism and isomorphism on Jordan Lie superalgebras. Moreover, some elementary properties and discriminating solutions on solvable, nilpotent, semisimple, sipmle Jordan Lie superalgebras are obtained, respectively.