Universal Enveloping Algebra Of Hom-Lie Sl(n, (?)), Hom-PBW Basis And 2-Cohomology Group Of Hom-Lie Sl(n, (?))

In this dissertation,we mainly construct the universal enveloping algebra of Hom-Lie sl(2,C) and consider its Hom-PBW type basis.By the same method,we similarly construct the universal enveloping algebra of Hom-Lie sl(n,C),and consider its Hom-PBW type basis.Finally,we discuss the central extensions of Hom-Lie sl(2,C) and Hom-Lie sl(n,C),and we prove both the 2-cohomology group of Hom-Lie sl(2,C) and the 2-cohomology group of Hom-Lie sl(n,C) with trivial coefficient are zero.This dissertation is organized as follows:In chapter 1 we talk about the background knowledge of Lie algebras and Hom-Lie algebras and introduce many authors' work on this topic,including the objective and the content of this dissertation.In chapter 2 we review some elemental knowledge of Hom-Lie algebras.In chapter 3 we talk about the knowledge of weighted tree and planner binary tree.In chapter 4 we construct the universal enveloping algebra of Hom-Lie sl(2,C) and consider its Hom-PBW type basis.In chapter 5 we construct the universal enveloping algebra of Hom-Lie sl(n,C) and consider its Hom-PBW type basis.In chapter 6 we discuss the central extensions of Hom-Lie sl(2,C) and Hom-Lie sl(n,C).