RIBBON STRUCTURES OF THE DRINFELD CENTER OF A FINITE TENSOR CATEGORY

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. Our result implies 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.