Some Properties Of Weak Vertex Algebras Over Fields Of Prime Characteristic

Vertex algebra is a very active research field in mathematics.Weak vertex algebra is a generalization of the concept of vertex algebra.In this paper,we mainly study weak vertex algebras over fields of prime characteristic,and obtain some basic properties of weak vertex algebras over fields of prime characteristic and their relations with the representations of vertex algebras.Finally,we discuss a class of weak vertex algebras and give an example of Z-graded weak vertex algebras.We generalize some properties of characteristic zero weak vertex algebra to fields of prime characteristic.