| The thesis mainly composed of two parts.In the first part,we study the split twisted inner derivation triple systems with no restrictions on their 0-root root space.Firstly,we define the root connections of the split twisted inner derivation triple system T.Secondly,using the property of root connection,the decomposition of T is obtained,that is.T=U+Σ[α]∈ΛT/～I[α],where U is subspace of T0,I[α]is the ideal of T,satisfying {I[α],T,I[β]}={T,I[α],I[β]}={I[α],I[β],T}={I[α],T,I[β]}’=[T,I[α],I[β]}’={I[α],I[β],T}’=0 if[α]≠[β].Finally,the concept of root-multiplicativity of split twisted inner derivation triple system is defined,and the necessary and sufficient condition for split twisted inner derivation triple system to be simple is obtained.In the second part,we study the split δ-Jordan Lie color triple systems.Firstly,we introduce the concept of split δ-Jordan Lie color triple system T.Secondly,we define the root connections of T,and using the property of root connection,the decomposition of T is obtained,that is,T=U+Σ[α]∈Λ1/～I[α],where U is subspace of T0,I[α]is the ideal of T,satisfying {I[α],T,I[[β]}={I[α],I[β],T}={T,I[α],I[β]}=0 if[α]≠[β].Finally,the concepts of maximum length and rootmultiplicativity of δ-Jordan Lie color triple system are defined,and the necessary and sufficient condition for split δ-Jordan Lie color triple system to be simple is obtained. |
