q-Virasoro algebra and affine Kac-Moody Lie algebras.

In this paper, we introduce an infinite-dimensional Lie algebra D S for any abelian group S. If S is the additive group of integers, D S reduces to the q -Virasoro algebra D q introduced by Belov and Chaltikian in the study of lattice conformal theories. Guided by the theory of equivariant quasi modules for vertex algebras, we introduce another Lie algebra g S with S as an automorphism group and we prove that D S is isomorphic to the S -covariant algebra of the affine Lie algebra g S ˆ. We then relate restricted D S -modules of level ℓ ∈ C to equivariant quasi modules for the vertex algebra V g S ˆ (ℓ , 0) associated to g S ˆ with level ℓ. Furthermore, we establish an intrinsic connection between the q -Virasoro algebra D q and affine Kac-Moody Lie algebras. More specifically, we show that if S is a finite abelian group of order 2 l + 1 , D S is isomorphic to the affine Kac-Moody algebra of type B l (1). [ABSTRACT FROM AUTHOR]