Pivotal structures of the Drinfeld center of a finite tensor category

Abstract

We classify the pivotal structures of the Drinfeld center $\mathcal{Z}(\mathcal{C})$ of a finite tensor category $\mathcal{C}$. As a consequence, every pivotal structure of $\mathcal{Z}(\mathcal{C})$ can be obtained from a pair $(\beta ,j)$ consisting of an invertible object $\beta$ of $\mathcal{C}$ and an isomorphism $j:\beta \otimes (-)\otimes {\beta }^{\ast }\to (-{)}^{\ast \ast }$ of monoidal functors.

arXiv comment29 pages, some xy-pic figures. v3: Many error are corrected. A remark on a categorification of the Rosenberg-Zelinsky exact sequence is added