循环带点融合范畴的图表学

Module categories over finite pointed tensor categories

We study exact module categories over the representation categories of finite-dimensional quasi-Hopf algebras. As a consequence we classify exact module categories over some families of pointed tensor categories with cyclic group of invertible objets of order p, where p is a prime number.

正特征下秩一 pointed Hopf 代数的精确分解，I

Exact Factorizations of Rank-One Pointed Hopf Algebras in Positive Characteristic, I

本文对正特征代数闭域上第三型秩一 pointed Hopf 代数的精确分解分类，通过匹配对研究，得到其与基础有限群精确分解的对应关系，并应用于Radford代数与素数阶循环群的精确分解确定。

From Projective Representations to Quasi-Quantum Groups

This is a contribution to the project of quiver approaches to quasi-quantum groups initiated in arXiv:0902.1620. We classify Majid bimodules over groups with 3-cocycles by virtue of projective representations. This leads to a theoretic classification of graded pointed Majid algebras over path coalgebras, or equivalently cofree pointed coalgebras, and helps to provide a projective representation-theoretic description of the gauge equivalence of graded pointed Majid algebras. We apply this machinery to construct some concrete examples and obtain a classification of finite-dimensional graded poin…

A class of prime fusion categories of dimension $2^N$

We study a class of strictly weakly integral fusion categories $\mathfrak{I}_{N, ζ}$, where $N \geq 1$ is a natural number and $ζ$ is a $2^N$th root of unity, that we call $N$-Ising fusion categories. An $N$-Ising fusion category has Frobenius-Perron dimension $2^{N+1}$ and is a graded extension of a pointed fusion category of rank 2 by the cyclic group of order $\mathbb Z_{2^N}$. We show that every braided $N$-Ising fusion category is prime and also that there exists a slightly degenerate $N$-Ising braided fusion category for all $N > 2$. We also prove a structure result for braided extension…

仿射A子因子平面代数的扭结理论

Skein Theory for Affine A Subfactor Planar Algebras

本研究推进Kuperberg纲领，给出指标为4的仿射A子因子平面代数的生成元与关系表示，以纯图解方式新证这类平面代数的存在数量及对应范畴的幺半等价性，提供全新图解方法。