Ribbon structures of the Drinfeld center of a finite tensor category

2017/07/31 by Kenichi Shimizu, Shimizu, Kenichi · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1707.09691

openalex publication_date 2017/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify the ribbon structures of the Drinfeld center Z(C) of a finite tensor category C. Our result generalizes Kauffman and Radford's classification result of the ribbon elements of the Drinfeld double of a finite-dimensional Hopf algebra. As a consequence, we see that Z(C) is a modular tensor category in the sense of Lyubashenko if C is a spherical finite tensor category in the sense of Douglas, Schommer-Pries and Snyder.

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