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Exact module categories over $\mathrm{Rep}(u_q(\mathfrak{sl}_2))$ (2503.21265v1)
Published 27 Mar 2025 in math.QA, math.CT, and math.RT
Abstract: 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.