A generalization of twisted modules over vertex algebras

Abstract

For an arbitrary positive integer T we introduce the notion of a (V,T)-module over a vertex algebra V, which is a generalization of a twisted V-module. Under some conditions on V, we construct an associative algebra A^T_m(V) for m ∈ (1/T)ℕ and an A^T_m(V)-A^T_n(V)-bimodule A^T_n,m(V) for n,m ∈ (1/T)ℕ and we establish a one-to-one correspondence between the set of isomorphism classes of simple left A^T₀(V)-modules and that of simple (1/T)ℕ-graded (V,T)-modules.