Engle's Theorem Of Jordan Lie Algebra And Its Applications

As a natural generalization of Lie superalgebras, Jordan Lie superalgebras and its properties were first given by S.Okubo and N.Kamiya in 1997[1].In this thesis, I give some properties of Jordan Lie algebra, prove that the Engle theorem of Jordan Lie algebra and apply it to obtain some properties on nilpotent Jordan Lie algebra. Furthermore, I give the definition and some properties of Cartan subalgebra on Jordan Lie algebra.