Research On The Quotient Algebra Of A Kind Of Tensor Algebra

In this paper,definitions and related conclusions of Virasoro algebras and Heisenberg algebras are recalled firstly.Then another more direct method to prove a fundamental theorem is given when we talk about the representation theory of Heisenberg algebras.The theorem is that M(1)(?)?M?M is a module isomorphism of Heisenberg algebra H.On the basis of the representation theory of Virasoro algebras,a basis of a typical quotient algebra A? of tensor algebras is studied.By mathematical induction,an associated algebra A? that is related to A? is constructed and the multiplication of A?is proved to be well-defined in an elementary way.Finally,the specific form of a basis of A? is given by using a homomorphism from A? to A?,which are monomials that satisfying certain ordinal relations.This paper is divided into five portions.In the first portion,the background and current situation of research contents in this paper are narrated.In the second portion,basic conceptions and the completely reducible representation of Virasoro algebras are recalled.In the third portion,basic conceptions and the irreducible module M(1,?)of Heisenberg algebras are discussed and the theorem that M(1)(?)?M?M is a module isomorphism of H is proved.In the fourth portion,the specific form of a basis of A? is explicitly proved and the unitary representation of Virasoro algebra is studied by means of the module V? of A?.In the fifth portion,a summary of main conclusions in this paper is given.