标题： 关于$\mathrm{Rep}(u_q(\mathfrak{sl}_2))$的精确模范畴 显示英文标题

标题： Exact module categories over $\mathrm{Rep}(u_q(\mathfrak{sl}_2))$

摘要： 我们给出了小量子群$\mathrm{Rep}(u_q(\mathfrak{sl}_2))$的表示的有限张量范畴上一组完全的不可分解的正合模范畴列表，其中$u_q(\mathfrak{sl}_2)$是一个带有奇数阶本原单位根的根$q$。 每个这样的范畴都明确地表现为由生成元和关系定义的$u_q(\mathfrak{sl}_2)$上左余模代数的表示范畴。 显示英文摘要

摘要： We give a complete list of indecomposable exact module categories over the finite tensor category $\mathrm{Rep}(u_q(\mathfrak{sl}_2))$ of representations of the small quantum group $u_q(\mathfrak{sl}_2)$, where $q$ is a root of unity of odd order. Each of them is given as the category of representations of a left comodule algebra over $u_q(\mathfrak{sl}_2)$ explicitly presented by generators and relations.