Fundamental Properties Of Axiomatic G₁-Vertex Algebras Over Fields Of Prime Characteristic

At present,the research results of vertex algebras on prime characteristic fields are relatively few.This paper mainly studies a class of nonlocal vertex algebras on prime characteristic field—axiomatic G1-vertex algebras,extends the research method of zero characteristic fields analogically to prime characteristic fields,and then studies axiomatic G1-vertex algebras on prime characteristic field.In this paper,we first give the definitions of axiomatic G1-vertex algebras and weak axiomatic G1-vertex algebras,and analyze the differences and connections between weak axiomatic G1-vertex algebras and axiomatic G1-vertex algebras.Secondly,we find an example of constructing axiomatic G1-vertex algebras by B-module algebras with derivation D,and then find some subalgebras and minimum subalgebras of weak axiomatic G1-vertex algebras by the definition of subalgebras and their equivalent definitions.Finally,we obtain some basic properties,such as conjugate formula and the difference and connection between(weak)axiomatic G1-vertex algebras and vertex algebras.