Reduced Tensor Product on the Drinfeld Center

Abstract

The annulus comes with a "stacking" operation which glues two annuli into one. This provides a tensor product structure on the category of boundary values $Z_{\text{CY}}(\text{Ann})$ associated to the annulus in an extended Crane-Yetter TQFT. It is known that $Z_{\text{CY}}(\text{Ann})\simeq \mathcal{Z}(\mathcal{A})$, the Drinfeld center of the premodular category $\mathcal{A}$ from which $Z_{\text{CY}}$ is constructed. We give an explicit formula for the tensor product on $\mathcal{Z}(\mathcal{A})$ that corresponds to the stacking operation on $Z_{\text{CY}}(\text{Ann})$.

arXiv commentupdate: revision for resubmission

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Cited by in corpus (5)

• Minimal nondegenerate extensions
• The Drinfeld Centre of a Symmetric Fusion Category is 2-Fold Monoidal
• The Symmetric Tensor Product on the Drinfeld Centre of a Symmetric Fusion Category
• On the Category of Boundary Values in the Extended Crane-Yetter TQFT
• Categorical Center of Higher Genera and 4D Factorization Homology