The Bialgebraic Structure Of Heisenberg-Virasoro Deformed Lie Algebra And Superalgebra

In this paper,basic concepts and related conclusions of Lie algebras,bialgebras,super algebras and super bialgebras are recalled firstly.We mainly study bialgebra structures of the Heisenberg-Virasoro deformed Lie algebra and super bialgebra structures of the super Heisenberg-Virasoro algebra in the complex field.The sufficient and necessary conditions for them to be triangular coboundary are obtained respectively.The content of this paper is divided into four sections.In the first chapter,the research background of this paper is given.We introduce the corresponding state,the development trend and also the research significance of the problems involved in this paper.In the second chapter,we introduce the deformed twisted Heisenberg-Virasoro algebra and study the derivatives of this type algebra to its own tensor algebra in order to describe the bialgebra structure(See Theorem 2.3.1,2.3.2).In the third chapter,we introduce super Heisenberg-Virasoro algebra and study the derivatives of this type super algebra to its own tensor algebra in order to describe the super bialgebra structure(See Theorem 3.3.1,3.3.2).In the last chapter,the main content of this paper is summarized.