q-Virasoro algebra and vertex algebras
q-Virasoro algebra and vertex algebras
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q-Virasoro 代数和顶点代数
DOI：
10.1016/j.jpaa.2014.06.004
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发表时间：
2015
影响因子：
0.8
通讯作者：
Wang Qing
中科院分区：
文献类型：
--
作者：
Guo Hongyan;Li Haisheng;Tan Shaobin;Wang Qing
本文在顶点代数的背景下，研究了Belov和Chaltikian引入并称为q-Virasoro代数的Virasoro代数的某种变形D.其中，我们证明了对于任意复数n，水平n的限制D-模范畴与某个仿射型顶点代数的拟模范畴正则同构。我们还证明了对于同一顶点代数，水平限制D-模范畴与Z-等变π-协调拟模范畴是典范同构的。在这个过程中，我们引入并使用了一个由生成元和关系定义的无限维李代数，并将其与gl∞的一个子代数明确地等同起来.
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∞.