The Symmetric Tensor Product on the Drinfeld Centre of a Symmetric Fusion Category
arXiv:1710.06461 · doi:10.1016/j.jpaa.2020.106348
Abstract
We define a symmetric tensor product on the Drinfeld centre of a symmetric fusion category, in addition to its usual tensor product. We examine what this tensor product looks like under Tannaka duality, identifying the symmetric fusion category with the representation category of a finite (super)-group. Under this identification, the Drinfeld centre is the category of equivariant vector bundles over the finite group (underlying the super-group, in the super case). In the non-super case, we show that the symmetric tensor product corresponds to the fibrewise tensor product of these vector bundles. In the super case, we define for each super-group structure on the finite group a super-version of the fibrewise tensor product. We show that the symmetric tensor product on the Drinfeld centre of the representation category of the resulting finite super-groups corresponds to this super-version of the fibrewise tensor product on the category of equivariant vector bundles over the finite group.
40 pages, many diagrams
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Cited by in corpus (7)
- Minimal nondegenerate extensions
- Topological Quantum Field Theories for character varieties
- Reduced Tensor Product on the Drinfeld Center
- The Drinfeld Centre of a Symmetric Fusion Category is 2-Fold Monoidal
- Drinfeld Centre-Crossed Braided Tensor Categories
- On the Category of Boundary Values in the Extended Crane-Yetter TQFT
- The Reduced Tensor Product of Braided Tensor Categories Containing a Symmetric Fusion Category