Q-Virasoro algebra and vertex algebras

Hongyan Guo, Haisheng Li, Shaobin Tan, Qing Wang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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∞.

Original languageEnglish (US)
Pages (from-to)1258-1277
Number of pages20
JournalJournal of Pure and Applied Algebra
Volume219
Issue number4
DOIs
StatePublished - Apr 1 2015

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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