Solvable Lie Triple Supersystems

In this thesis, I give some basic conceptions and important properties of Lie triple supersystems and discuss the relationships between Lie triple supersystems and Lie superalgebras. Moreover, I give the classification of 2-dimensional Lie triple supersystems over C and obtain some important properties of Lie triple supersystems which are by no means true for Lie superalgebras.The main results in this paper are the following:Theoreml Let T be a Lie triple supersystem and suppose that I is an ideal of T,then [T, I, I] is an ideal of T.Theorem2 Let T be a Lie triple supersystem.1) Suppose that I and I arc solvable ideals of T , then I + I is an solvable ideals of T.2) If T be a finite-dimensional Lie triple supersystem, then there exists uniqueness maximal solvable ideal R of T ,for all solvable ideal I such that I (?) R.Theorem3 Let T be a Lie triple supersystem and suppose that I is an ideal of T,then the following statements hold: 1) There exists ideals array of T ,which2) I (?) I, (?) N.Theorem4 Let T be a two-dimensional Lie triple system over C,and dim[T,T,T] = 2,then we have1) T is a simple Lie triple system.2) T is isomorph with the following linear Lie triple system...