Abstract
We classify the ribbon structures of the Drinfeld center $\mathcal{Z}(\mathcal{C})$ of a finite tensor category $\mathcal{C}$. Our result generalizes Kauffman and Radford's classification result of the ribbon elements of the Drinfeld double of a finite-dimensional Hopf algebra. Our result implies that $\mathcal{Z}(\mathcal{C})$ is a modular tensor category in the sense of Lyubashenko if $\mathcal{C}$ is a spherical finite tensor category in the sense of Douglas, Schommer-Pries and Snyder.
Funding Statement
The author is supported by JSPS KAKENHI Grant Number 16K17568 and JP20K03520.
Acknowledgment
The author thanks the referee for careful reading of the manuscript.
Citation
Kenichi Shimizu. "Ribbon structures of the Drinfeld center of a finite tensor category." Kodai Math. J. 46 (1) 75 - 114, March 2023. https://doi.org/10.2996/kmj46106
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