论文标题
一致的处理机体组表示系统的分类
Classification of Consistent Systems of Handlebody Group Representations
论文作者
论文摘要
手柄组的分类空间形成一个模块化的作战。手柄式oprad的代数在与胶合兼容的手柄组的表示系统中产生。我们证明，在任意对称的单体bigicategory $ \ mathcal {m} $中具有值的车把的模块化库（我们介绍这些名称ansular functor）等于自二平衡均衡的编织代数等于$ \ nathcal {m} $。在专门针对线性框架之后，这证明了有限维矢量空间上的句柄群体表示系统的一致系统等同于Boyarchenko-Drinfeld意义上的功能区Grothendieck-Verdier类别。此外，就lyubashenko coend的概括而言，它为分配给任意手柄的向量空间产生了一个具体公式。我们的主要结果可用于从符合轻度有限条件下的顶点操作员代数中获取呈函数。这包括顶点操作员代数的示例，其表示类别具有非脱颖而出的单体产物。
The classifying spaces of handlebody groups form a modular operad. Algebras over the handlebody operad yield systems of representations of handlebody groups that are compatible with gluing. We prove that algebras over the modular operad of handlebodies with values in an arbitrary symmetric monoidal bicategory $\mathcal{M}$ (we introduce for these the name ansular functor) are equivalent to self-dual balanced braided algebras in $\mathcal{M}$. After specialization to a linear framework, this proves that consistent systems of handlebody group representations on finite-dimensional vector spaces are equivalent to ribbon Grothendieck-Verdier categories in the sense of Boyarchenko-Drinfeld. Additionally, it produces a concrete formula for the vector space assigned to an arbitrary handlebody in terms of a generalization of Lyubashenko's coend. Our main result can be used to obtain an ansular functor from vertex operator algebras subject to mild finiteness conditions. This includes examples of vertex operator algebras whose representation category has a non-exact monoidal product.
