The symmetric tensor product on the Drinfeld centre of a symmetric fusion category

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Wasserman, Thomas A.¹ 

[1] Univ Copenhagen, Math Inst, Univ Pk 5, DK-2300 Copenhagen, Denmark

关键词: Fusion categories;    Drinfeld centre;   

DOI  :  10.1016/j.jpaa.2020.106348

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier B.V. All rights reserved.

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