Pivotal structures of the Drinfeld center of a finite tensor category

TL;DR

This paper classifies the pivotal structures of the Drinfeld center of a finite tensor category, showing they can be described using invertible objects and specific monoidal isomorphisms.

Contribution

It provides a complete classification of pivotal structures in the Drinfeld center, linking them to pairs of invertible objects and monoidal functor isomorphisms.

Findings

Every pivotal structure arises from a pair $(eta, j)$

Classification is explicit and constructive

Connects pivotal structures to invertible objects and monoidal isomorphisms

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 $j: \beta \otimes (-) \otimes \beta^* \to (-)^{**}$ of monoidal functors.