Ribbon structures of the Drinfeld center of a finite tensor category

Abstract

We classify the ribbon structures of the Drinfeld center of a finite tensor category . 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 is a modular tensor category in the sense of Lyubashenko if is a spherical finite tensor category in the sense of Douglas, Schommer-Pries and Snyder.