Drinfeld centers of fusion categories arising from generalized Haagerup subfactors

Quantum topology

article

Pinhas Grossman¹  Masaki Izumi² 

[1] University of New South Wales;Kyoto University

关键词: Subfactors;    fusion categories;    Cuntz algebras;   

DOI  :  10.4171/qt/167

学科分类：内科医学

来源: European Mathematical Society

【 摘 要 】

We consider generalized Haagerup categories such that 1⊕X1 \oplus X1⊕X admits a QQQ-system for every non-invertible simple object XXX. We show that in such a category, the group of order two invertible objects has size at most four. We describe the simple objects of the Drinfeld center and give partial formulas for the modular data. We compute the remaining corner of the modular data for several examples and make conjectures about the general case. We also consider several types of equivariantizations and de-equivariantizations of generalized Haagerup categories and describe their Drinfeld centers. In particular, we compute the modular data for the Drinfeld centers of a number of examples of fusion categories arising in the classification of small-index subfactors: the Asaeda–Haagerup subfactor; the 3Z43^{\mathbb{Z}_4}3Z4​ and 3Z2×Z23^{\mathbb{Z}_2 \times \mathbb{Z}_2}3Z2​×Z2​ subfactors; the 2D22D22D2 subfactor; and the 444244424442 subfactor. The results suggest the possibility of several new infinite families of quadratic categories. A description and generalization of the modular data associated to these families in terms of pairs of metric groups is taken up in the accompanying paper [Comm. Math. Phys. 380 (2020), 1091–1150].

【 授权许可】

CC BY