Exact module categories over Rep(u_q(\mathfraksl₂))

2025/03/27 by Daisuke Nakamura, Nakamura, Daisuke, Taiki Shibata +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics #Computer science #Mathematics #Physics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2503.21265

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We give a complete list of indecomposable exact module categories over the finite tensor category Rep(u_q(\mathfraksl₂)) of representations of the small quantum group u_q(\mathfraksl₂), 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(\mathfraksl₂) explicitly presented by generators and relations.

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