TY - JOUR

T1 - Q-Virasoro algebra and vertex algebras

AU - Guo, Hongyan

AU - Li, Haisheng

AU - Tan, Shaobin

AU - Wang, Qing

N1 - Publisher Copyright:
© 2014 Elsevier B.V.

PY - 2015/4/1

Y1 - 2015/4/1

N2 - 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∞.

AB - 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∞.

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U2 - 10.1016/j.jpaa.2014.06.004

DO - 10.1016/j.jpaa.2014.06.004

M3 - Article

AN - SCOPUS:84916217168

VL - 219

SP - 1258

EP - 1277

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 4

ER -