Hom-structures On The Two Kinds Of Lie Algebras And Quantum Group Structures And Intermediate Sequence Modules Over The Two-parameter Deformed Virasoro Algebra Of Hom-type

This paper mainly studies the structure theory and representation theory of Hom-Lie algebra.First of all,We study the Hom-Lie algebraic structures on the 2n+4-dimensional Schr?dinger algebra,and determine the existence of nontrivial Hom-Lie algebraic structures on the 2n+4 dimensional Schr?dinger algebra.Secondly,we study the structure of Hom-Lie algebra on the twisted Schr?dinger-Virasoro algebra,and determine the existence of nontrivial Hom-Lie algebraic structure on the twisted Schr?dinger-Virasoro algebra.Furthermore,we construct a two-parameter deformed Virasoro algebra by using the bosonic oscillators,which is Hom-Lie algebra,and we construct the nontrivial Hopf structure on the two-parameter deformed Virasoro algebra.Finally,we construct a class of indecomposable Harish-Chandra modules with a weight space of dimension one on the two-parameter deformed Virasoro algebra,and classify these modules.