论文标题
在低级融合戒指上
On Low Rank Fusion Rings
论文作者
论文摘要
我们提出了一种生成特定等级和多样性的融合环的方法。该方法用于生成详尽的融合环列表，直到9个多重性。我们基于在集合上具有传递作用的组引入了一类非交通融合环。这概括了Tambara-Yamagami（Ty）和Haagerup-izumi（HI）融合环。我们举例说明了这样的环，该戒指可分类，而不是TY或HI类型。审查了与亚组的非交通融合环的结构，并将一个组的一个和两粒子扩展分类。引入了一个包含有关融合环数据的网站，并提供了用于与这些环一起工作的Wolfram语言包的概述。
We present a method to generate all fusion rings of a specific rank and multiplicity. This method was used to generate exhaustive lists of fusion rings up to order 9 for several multiplicities. We introduce a class of non-commutative fusion rings based on a group with transitive action on a set. This generalizes the Tambara-Yamagami (TY) and Haagerup- Izumi (HI) fusion rings. We give an example of such a ring which is categorifiable and is not of TY or HI type. The structure of non-commutative fusion rings with a subgroup is reviewed, and the one-and two-particle extensions of groups are classified. A website containing data on fusion rings is introduced, and an overview of a Wolfram Language package for working with these rings is given.
