Several Types Of Subalgebras Of Modular Vertex Algebras

Vertex algebra is an algebraic structure introduced by Borcherds in 1986.Deeply related to many mathematical and physical branches,vertex algebra has attracted more and more attention.The research on vertex algebra generally focuses on complex fields,however,the research on vertex algebra over prime characteristic fields(modular vertex algebra)has become very popular in recent years.In this paper,we mainly study several types of subalgebras of Virasoro vertex algebras,affine vertex algebras,Heisenberg vertex algebras and modular vertex algebras associated with W-algebra W(2,2),including subalgebras related to the centers,and subalgebras related to the p-centers.In addition,we study the properties of these subalgebras,and further study the relationship between these subalgebras and vertex Leibniz algebras,vacuum-free vertex algebras,and vertex algebras without vacuum.