Decomposition And Simplicity Of Two Classes Of Split BiHom Lie Type Algebras

The thesis mainly composed of two parts.In the first part,we study the split regular BiHom-Lie color algebras with symmetric roots.Firstly,we introduce the concept of split regular BiHom-Lie color algebras.Secondly,two non-zero root connections are defined,and it is proved that root connection relationship is the equivalent relationship of root system.Then,taking the root connection as a instrument,the decomposition ofis obtained,that is,if(5（）=0,=_∈[-1,_--1],then=⊕[]∈/～[],where(5（）is the center of,is the maximal commutative subalgebra of,_[]is the ideal of.Finally,the concepts of maximum length and root integrability of this kind of algebra are defined,and the simplicity ofwith maximum length and root integrability is described.In the second part,we study the split regular BiHom-Poisson color algebras with symmetric roots.Firstly,we introduce the concept of split regular BiHom-Poisson color algebras.Secondly,two non-zero root connections are defined,and it is proved that root connection relationship is the equivalent relationship of root system.Then,taking the root connection as a instrument,the decomposition ofis obtained,that is,if(5（）=0,=_∈([-1,_--1]+-1_--1),then=⊕[]∈/～[],where(5（）is the center of,is the maximal commutative subalgebra of,_[]is the ideal of.Finally,the concepts of maximum length and root integrability of this kind of algebra are defined,and the simplicity ofwith maximum length and root integrability is described.