2022/07/26 by Shinji Koshida, Koshida, Shinji
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Physics of Superconductivity and Magnetism #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2207.12969
openalex publication_date 2022/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove the equivalence between two ribbon tensor categories. On the one hand, we consider the category of modules of the Virasoro vertex operator algebra with generic central charge (generic Virasoro VOA) generated by those simple modules lying in the first row of the Kac table. On the other hand, we take the category of finite-dimensional type I modules of the quantum group Uq (\mathfraksl2) with q determined by the central charge. This is a continuation of our previous work in which we examined intertwining operators for the generic Virasoro VOA in detail. Our strategy to show the categorical equivalence is to take those results as input and directly compare the structures of tensor categories. Therefore, we are to execute the most elementary proof of categorical equivalence. We also study the category of C1-cofinite modules of the generic Virasoro VOA. We show that it is ribbon equivalent to the category of finite-dimensional type I modules of Uq (\mathfraksl2)⊗ U_q(\mathfraksl2), where q and q are again related to the central charge.