论文标题
全球尺寸的模块化融合类别$ p^2 $
Pre-modular fusion categories of global dimensions $p^2$
论文作者
论文摘要
令$ p \ geq5 $为素数，我们表明，一个未指控的模块化融合类别$ \ nathcal {c} $是grothendieck，相当于$ \ mathcal {c}（\ mathfrak {sl} {sl} _2,2,2（p-1）_2,2（p-1）） $ u $是某种完全积极的代数单位，$ a $是坦纳基亚子类别的常规代数$ \ text {rep}（\ m athbb {z} _2）\ subseteq \ subseteq \ subseteeq \ mathcal {c}（c}（\ mathfrak {slfrak {sl} {sl} _2,2,2（p-1））$。作为直接推论，我们对全球尺寸的非简单模块化融合类别进行分类$ p^2 $。
Let $p\geq5$ be a prime, we show that a non-pointed modular fusion category $\mathcal{C}$ is Grothendieck equivalent to $\mathcal{C}(\mathfrak{sl}_2,2(p-1))_A^0$ if and only if $\dim(\mathcal{C})=p\cdot u$, where $u$ is a certain totally positive algebraic unit and $A$ is the regular algebra of the Tannakian subcategory $\text{Rep}(\mathbb{Z}_2)\subseteq\mathcal{C}(\mathfrak{sl}_2,2(p-1))$. As a direct corollary, we classify non-simple modular fusion categories of global dimensions $p^2$.
