论文标题
通用Virasoro VOA和量子组的模块类别
Module Categories of the Generic Virasoro VOA and Quantum Groups
论文作者
论文摘要
在本文中，我们证明了两个色带张量类别之间的等效性。一方面，我们考虑了带有通用中央电荷（通用Virasoro voa）的Virasoro顶点操作员代数的模块类别，该模块由位于KAC表的第一行中的那些简单模块产生。另一方面，我们将量子组$ \ mathcal {u} _q（\ Mathfrak {sl} _ {2}）$的有限维I型I模块进行$ q $。这是我们以前的工作的延续，我们详细介绍了通用Virasoro VOA的交织操作员。我们表明分类等效性的策略是将这些结果作为输入并直接比较张量类别的结构。因此，我们将执行最基本的分类等效证明。我们还研究了$ c_ {1} $的类别 - 通用Virasoro VOA的Cofinite模块。我们表明，它是$ \ Mathcal {u} _q（\ Mathfrak {sl} _ {2}）\ otimes \ Mathcal {U} _ { $ \ tilde {q} $再次与中央费用有关。
In this paper, we prove the equivalence between two ribbon tensor categories. On the one hand, we consider the category of modules of the Virasoro vertex operator algebra with generic central charge (generic Virasoro VOA) generated by those simple modules lying in the first row of the Kac table. On the other hand, we take the category of finite-dimensional type I modules of the quantum group $\mathcal{U}_q (\mathfrak{sl}_{2})$ with $q$ determined by the central charge. This is a continuation of our previous work in which we examined intertwining operators for the generic Virasoro VOA in detail. Our strategy to show the categorical equivalence is to take those results as input and directly compare the structures of tensor categories. Therefore, we are to execute the most elementary proof of categorical equivalence. We also study the category of $C_{1}$-cofinite modules of the generic Virasoro VOA. We show that it is ribbon equivalent to the category of finite-dimensional type I modules of $\mathcal{U}_q (\mathfrak{sl}_{2})\otimes \mathcal{U}_{\tilde{q}}(\mathfrak{sl}_{2})$, where $q$ and $\tilde{q}$ are again related to the central charge.
