Classifying fusion categories ⊗-generated by an object of small Frobenius–Perron dimension
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Cain Edie-Michell [1]
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[1] Vanderbilt University
Vanderbilt University
Estados Unidos
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- Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 2, 2020
- Idioma: inglés
- DOI: 10.1007/s00029-020-0550-3
- Enlaces
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Resumen
The goal of this paper is to classify fusion categories C which are ⊗-generated by an object X of Frobenius–Perron dimension less than 2, with the additional mild assumption that the adjoint subcategory of C is ⊗-generated by the object X⊗X∗. This classification has recently become accessible due to a result of Morrison and Snyder, showing that any such category must be a cyclic extension of a category of adjoint ADE type. Our main tools in this classification are the results of Etingof et al. (Quantum Topol 1(3);209–273, 2010. https://doi.org/10.4171/QT/6), classifying cyclic extensions of a given category in terms of data computed from the Brauer–Picard group, and Drinfeld centre of that category, and the results of Edie-Michell (Int. J. Math. 29(5):1850036, 2018. https://doi.org/10.1142/S0129167X18500362) which compute the Brauer–Picard group and Drinfeld centres of the categories of adjoint ADE type. Our classification includes the expected categories, constructed from cyclic groups and the categories of ADE type. More interestingly we have categories in our classification that are non-trivial de-equivariantizations of these expected categories. Most interesting of all, our classification includes three infinite families constructed from the exceptional quantum subgroups E4 of C(sl4,4), and E16,6 of C(sl2,16)⊠C(sl3,6).
