On certain generalizations of twisted affine Lie algebras and quasimodules for [formula omitted]-vertex algebras

Abstract

We continue a previous study on Γ -vertex algebras and their quasimodules. In this paper we refine certain known results and we prove that for any Z -graded vertex algebra V and a positive integer N , the category of V -modules is naturally isomorphic to the category of quasimodules of a certain type for V ⊗ N . We also study certain generalizations of twisted affine Lie algebras and we relate such Lie algebras to vertex algebras and their quasimodules, in a way similar to how twisted affine Lie algebras are related to vertex algebras and their twisted modules.