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

Daisuke Nakamura; Taiki Shibata; Kenichi Shimizu

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arXiv · 2503.21265

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

Daisuke Nakamura·Taiki Shibata·Kenichi Shimizu

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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.

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Daisuke Nakamura, Taiki Shibata, Kenichi Shimizu. 2025-03-27. Exact module categories over $\mathrm{Rep}(u_q(\mathfrak{sl}_2))$. https://arxiv.org/abs/2503.21265

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