Title: Ribbon structures of the Drinfeld center of a finite tensor category,
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. As a
consequence, we see 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.