A generalization of twisted modules over vertex algebras

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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 ATm(V) for m ∈ (1/T)ℕ and an ATm(V)-ATn(V)-bimodule ATn,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 AT0(V)-modules and that of simple (1/T)ℕ-graded (V,T)-modules.

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