发表机构
University of Alberta; SUNY-Plattsburgh; Max-Planck-Institut für Mathematik（阿尔伯塔大学; 纽约州立大学普拉茨堡分校; 马克斯·普朗克数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了奇数阶循环群的Haagerup-Izumi融合范畴，分类其可分代数，证明Evans-Gannon猜想，并给出奇数N≤43的完整HI范畴列表，同时否定了Davidovich-Hagge-Wang猜想。
AI 中文摘要
对于每个奇数$N$，我们利用Barnes双正弦函数构造了$\mathbb Z/N$的Haagerup-Izumi（HI）范畴。等变化给出了每个奇数$N$的$((\mathbb Z/N)^2,N^2)$型近群范畴。我们在此类HI范畴中分类了直到Morita等价的可分代数，并描述了它们的对偶范畴。这些对偶范畴通常是非循环群上具有非平凡点态结合子的HI范畴。我们证明了Evans-Gannon猜想，即中心的模数据总是涉及阶为$N^2+4$的有限度量群的破碎和，并直接从HI范畴的数据中恢复该群及其二次型。我们还给出了任意特征下的HI方程和重构，并证明了特征二中的Frobenius对称性。利用这一点，我们得到了奇数$N\le 43$上$\mathbb{C}$上的（未扭曲、子因子型）HI范畴的完整列表。其他应用包括找到三个两两非Morita等价的$\mathbb Z/15$范畴，其中心具有相同的模数据。我们证明了$\mathbb Z/5$ HI范畴的中心不能在分圆域上定义（即不允许分裂ribbon形式），从而否定了Davidovich-Hagge-Wang的一个猜想。
英文摘要
For every odd $N$, we construct a Haagerup-Izumi (HI) category for $\mathbb Z/N$, using Barnes double-sine functions. Equivariantization gives near-group categories of type $((\mathbb Z/N)^2,N^2)$ for every odd $N$. We classify connected separable algebras up to Morita equivalence in such HI categories and describe their dual categories. These duals are often HI for noncyclic groups with nontrivial pointed associators. We prove the Evans-Gannon conjecture that the modular data of the center is always a smashed sum involving a finite metric group of order $N^2+4$ and recover this group and its quadratic form directly from the data of the HI category. We also give the HI equations and reconstruction in arbitrary characteristic and prove a Frobenius symmetry in characteristic two. Using this, we obtain the complete list of (untwisted, subfactor type) HI categories over $\mathbb{C}$ for odd $N\le 43$. Other applications include finding three pairwise non-Morita-equivalent $\mathbb Z/15$ categories whose centers have the same modular data. We show that the center of a $\mathbb Z/5$ HI category cannot be defined (i.e., admits no split ribbon form) over a cyclotomic field, disproving a conjecture of Davidovich-Hagge-Wang.
Comments32 pages + appendices, comments welcome
