Research On Conformal Hyperalgebra Related Problems

The main content of this paper belongs to vertex algebra and its related fields.Firstly,the basic properties of state-field correspondence are discussed.On this basis,the concept of conformal super-algebra is introduced,and the close relationship between these two concepts is studied.Then the concept of locality of Laurent-series is extended,and some concrete examples of it are given.Finally,as the main result of this paper,a universal loop state–field correspondence is constructed by using tensor product,and its local properties are explored.This paper is divided into four portions:The first chapter mainly gives the research background and domestic and foreign research trends of the content involved in this paper.Then the specific research content and significance is expounded.In the second chapter,the preliminary of state-field correspondence and its correlation are given.In the third chapter,according to the definition of Lie conformal super-algebra,the definition of conformal super-algebra is obtained.Corresponding to the case of vertex algebra or vertex operator algebra,the locality of Laurent-series is generalized.According to the equivalent definition of vertex algebra,a class of vertex algebra is constructed.The fourth chapter concludes the primary content of this paper and prospect the approaching research subjects.