Modular Vertex Algebras Associated To The W-algebra W(2,2)

In this paper,we study vertex algebras VW(2,2)(c,0,0)associated to W(2,2)over a field of prime characteristic,and establish the relationship between the rep-resentations of such modular vertex algebras and the representations of W(2,2),so as to generalize certain results over fields of characteristic 0 to the case of prime characteristic.After that,we prove that W(2,2)has a restricted Lie algebra struc-ture,and on this basis we construct a class of ideals of modular vertex algebras VW(2,2)(c,0,0),and obtain a class of quotient algebras of VW(2,2)(c,0,0).