论文标题
来自非偏simimple tqfts的映射类组表示
Mapping Class Group Representations From Non-Semisimple TQFTs
论文作者
论文摘要
在[Arxiv：1912.02063]中，我们使用不一定是半密布模块化类别构建了三维拓扑量子场理论（TQFTS）。在这里，我们研究了这些TQFTS定义的映射表面类的投影表示形式，并通过基础模块类别$ \ MATHCAL {C} $的代数数据表达了一组发电机的作用。这使我们能够证明[arxiv：1912.02063]的非偏smisimimple tqfts引起的投射表示等同于lyubashenko通过[arxiv：arxiv：hepth/9405167]中的发电机和关系获得的。最后，我们表明，当$ \ mathcal {c} $是$ \ mathfrak {sl} _2 $的小量子组的有限维表示类别时，所有dehn twist for Surfaces for Surfaces的动作没有明显的点的无限顺序。
In [arXiv:1912.02063], we constructed 3-dimensional Topological Quantum Field Theories (TQFTs) using not necessarily semisimple modular categories. Here, we study projective representations of mapping class groups of surfaces defined by these TQFTs, and we express the action of a set of generators through the algebraic data of the underlying modular category $\mathcal{C}$. This allows us to prove that the projective representations induced from the non-semisimple TQFTs of [arXiv:1912.02063] are equivalent to those obtained by Lyubashenko via generators and relations in [arXiv:hep-th/9405167]. Finally, we show that, when $\mathcal{C}$ is the category of finite-dimensional representations of the small quantum group of $\mathfrak{sl}_2$, the action of all Dehn twists for surfaces without marked points has infinite order.
