论文标题
从Orbifold数据构建模块化类别
Constructing modular categories from orbifold data
论文作者
论文摘要
在Carqueville等人，Arxiv：1809.01483中，在模块化融合类别中的Orbifold Datum $ \ Mathbb {a} $的概念是作为Reshetikhin-Turaev tqfts的广义orbifold构造的一部分引入的。在本文中，给定一个简单的Orbifold Datum $ \ Mathbb {a} $中的$ \ Mathcal {C} $，我们引入了功能区类别$ \ MATHCAL {C} _ {\ MATHBB {A}} $，并再次显示它是一个模块化的融合类别。 $ \ Mathcal {C} _ {\ Mathbb {a}} $的定义是由Wilson Lines在广义Orbifold中的属性激励的。我们详细分析了两个示例：（i）当$ \ mathbb {a} $由简单的交换$δ$ -Separable frobenius algebra $ a $ in $ \ mathcal {c} $给出时； （ii）当$ \ mathbb {a} $是$ \ mathcal {c} = \ operatoTorname {vect} $中的Orbifold基准，它是由球形融合类别$ \ mathcal {s} $构建的。我们表明，在（i），$ \ mathcal {c} _ {\ mathbb {a}} $与$ a $的本地模块的类别相等，而在（ii）的类别上，则是$ \ mathcal {s} $的drinfeld中心。类别$ \ mathcal {c} _ {\ Mathbb {a}} $因此将这两个构造统一为单个代数设置。
In Carqueville et al., arXiv:1809.01483, the notion of an orbifold datum $\mathbb{A}$ in a modular fusion category $\mathcal{C}$ was introduced as part of a generalised orbifold construction for Reshetikhin-Turaev TQFTs. In this paper, given a simple orbifold datum $\mathbb{A}$ in $\mathcal{C}$, we introduce a ribbon category $\mathcal{C}_{\mathbb{A}}$ and show that it is again a modular fusion category. The definition of $\mathcal{C}_{\mathbb{A}}$ is motivated by properties of Wilson lines in the generalised orbifold. We analyse two examples in detail: (i) when $\mathbb{A}$ is given by a simple commutative $Δ$-separable Frobenius algebra $A$ in $\mathcal{C}$; (ii) when $\mathbb{A}$ is an orbifold datum in $\mathcal{C} = \operatorname{Vect}$, built from a spherical fusion category $\mathcal{S}$. We show that in case (i), $\mathcal{C}_{\mathbb{A}}$ is ribbon-equivalent to the category of local modules of $A$, and in case (ii), to the Drinfeld centre of $\mathcal{S}$. The category $\mathcal{C}_{\mathbb{A}}$ thus unifies these two constructions into a single algebraic setting.
