论文标题
带有瞬态galois动作的模块化类别
Modular categories with transitive Galois actions
论文作者
论文摘要
在本文中，我们研究了模块化类别，其对简单对象的Galois组动作是传递的。我们表明，这种模块化类别将独特的分解纳入主要的横向因素。 $ sl_2（\ mathbb {z}）$的表示形式证明是最小和不可修复的。与Verlinde公式一起，我们将Prime透射模块类别表征为量子组模块类别的伴随子类别的GALOIS共轭物$ \ Mathcal {C}（\ Mathfrak {slfrak {SL} _2，p-2）$，对于某些Prime prime $ P> 3 $。结果，我们完全分类了传递模块化类别。可以类似地定义超模块化类别的传递性。将获得任何及物化的超模块化类别的独特分解为s简单的透射因子，并且分裂的透射式超模块化类别被完全分类。
In this paper, we study modular categories whose Galois group actions on their simple objects are transitive. We show that such modular categories admit unique factorization into prime transitive factors. The representations of $SL_2(\mathbb{Z})$ associated with transitive modular categories are proven to be minimal and irreducible. Together with the Verlinde formula, we characterize prime transitive modular categories as the Galois conjugates of the adjoint subcategory of the quantum group modular category $\mathcal{C}(\mathfrak{sl}_2,p-2)$ for some prime $p > 3$. As a consequence, we completely classify transitive modular categories. Transitivity of super-modular categories can be similarly defined. A unique factorization of any transitive super-modular category into s-simple transitive factors is obtained, and the split transitive super-modular categories are completely classified.
