Pivotal structures of the Drinfeld center of a finite tensor category

Kenichi Shimizu

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arXiv · 1608.05905

Pivotal structures of the Drinfeld center of a finite tensor category

Kenichi Shimizu

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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.

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Kenichi Shimizu. 2016-08-21. Pivotal structures of the Drinfeld center of a finite tensor category. https://arxiv.org/abs/1608.05905

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