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

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Standard

The symmetric tensor product on the Drinfeld centre of a symmetric fusion category. / Wasserman, Thomas A.

In: Journal of Pure and Applied Algebra, Vol. 224, No. 8, 106348, 2020.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Wasserman, TA 2020, 'The symmetric tensor product on the Drinfeld centre of a symmetric fusion category', Journal of Pure and Applied Algebra, vol. 224, no. 8, 106348. https://doi.org/10.1016/j.jpaa.2020.106348

APA

Wasserman, T. A. (2020). The symmetric tensor product on the Drinfeld centre of a symmetric fusion category. Journal of Pure and Applied Algebra, 224(8), [106348]. https://doi.org/10.1016/j.jpaa.2020.106348

Vancouver

Wasserman TA. The symmetric tensor product on the Drinfeld centre of a symmetric fusion category. Journal of Pure and Applied Algebra. 2020;224(8). 106348. https://doi.org/10.1016/j.jpaa.2020.106348

Author

Wasserman, Thomas A. / The symmetric tensor product on the Drinfeld centre of a symmetric fusion category. In: Journal of Pure and Applied Algebra. 2020 ; Vol. 224, No. 8.

Bibtex

@article{2fa42584568d4f0db10aae12177ff394,
title = "The symmetric tensor product on the Drinfeld centre of a symmetric fusion category",
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.",
keywords = "Drinfeld centre, Fusion categories",
author = "Wasserman, {Thomas A.}",
year = "2020",
doi = "10.1016/j.jpaa.2020.106348",
language = "English",
volume = "224",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier BV * North-Holland",
number = "8",

}

RIS

TY - JOUR

T1 - The symmetric tensor product on the Drinfeld centre of a symmetric fusion category

AU - Wasserman, Thomas A.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Drinfeld centre

KW - Fusion categories

UR - http://www.scopus.com/inward/record.url?scp=85080044991&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2020.106348

DO - 10.1016/j.jpaa.2020.106348

M3 - Journal article

AN - SCOPUS:85080044991

VL - 224

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 8

M1 - 106348

ER -

ID: 260678015