一些秩为3的非辫型融合范畴
几何拓扑
2007-09-24 v2 量子代数
摘要
我们对具有三种简单对象类型的给定融合规则集的所有融合范畴进行了分类。如果Ostrik的一个猜想成立，我们的分类就完成了对具有三种简单对象类型的融合范畴的分类。为便于讨论，我们描述了一种方便、具体且实用的融合范畴图形演算变体，在此框架下讨论了枢轴性和球面性，并给出了四重对偶函子自然同构于恒等函子这一事实的一个简短而初等的重新证明。
引用
@article{arxiv.0704.0208,
title = {Some non-braided fusion categories of rank 3},
author = {Tobias J. Hagge and Seung-Moon Hong},
journal= {arXiv preprint arXiv:0704.0208},
year = {2007}
}
备注
18 pages, 7 figures, v2. Many expository improvements based on referee feedback, most notably to the proof of the main theorem and the section on pivotal structures. Fewer details are left to the reader. A new section outlines the structure of the proof of the main theorem and its relation to other results in the paper