q-Virasoro algebra and vertex algebras.

In this paper, we study a certain deformation D of the Virasoro algebra that was introduced and called q -Virasoro algebra by Belov and Chaltikian, in the context of vertex algebras. Among the main results, we prove that for any complex number ℓ , the category of restricted D -modules of level ℓ is canonically isomorphic to the category of quasi modules for a certain vertex algebra of affine type. We also prove that the category of restricted D -modules of level ℓ is canonically isomorphic to the category of Z -equivariant ϕ -coordinated quasi modules for the same vertex algebra. In the process, we introduce and employ a certain infinite dimensional Lie algebra which is defined in terms of generators and relations and then identified explicitly with a subalgebra of gl ∞ . [ABSTRACT FROM AUTHOR]