Abstract
To give a unified treatment on the association of Lie algebras and vertex algebras, we study (G,χϕ)-equivariant ϕ-coordinated quasi modules for vertex algebras, where G is a group with χϕ a linear character of G and ϕ is an associate of the one-dimensional additive formal group. The theory of (G,χϕ)-equivariant ϕ-coordinated quasi modules for nonlocal vertex algebra is established in [10]. In this paper, we concentrate on the context of vertex algebras. We establish several conceptual results, including a generalized commutator formula and a general construction of vertex algebras and their (G,χϕ)-equivariant ϕ-coordinated quasi modules. Furthermore, for any conformal algebra C, we construct a class of Lie algebras Cˆϕ[G] and prove that restricted Cˆϕ[G]-modules are exactly (G,χϕ)-equivariant ϕ-coordinated quasi modules for the universal enveloping vertex algebra of C. As an application, we determine the (G,χϕ)-equivariant ϕ-coordinated quasi modules for affine and Virasoro vertex algebras.
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