论文标题
按一个维度扩展的积分组环的分类
Categorification of integral group rings extended by one dimension
论文作者
论文摘要
有限组的整体组环$ \ mathbb {z} g $ $ g $恰恰是那些融合戒指的基础元素具有frobenius-perron尺寸1，并且每个融合都可以分类，因为它作为融合类别的grothenieck ring产生。在这里，我们分析了融合环的结构和表示理论的基础，其frobenius-perron尺寸完全不同于1的值。我们的目标是一组结果，有助于表征当该融合环可分类时表征。作为概念验证，我们将无限的Abelian群体集合的可分类近组融合环分类，这项任务仅针对三个这样的群体完成。
The integral group rings $\mathbb{Z}G$ for finite groups $G$ are precisely those fusion rings whose basis elements have Frobenius-Perron dimension 1, and each is categorifiable in the sense that it arises as the Grothendieck ring of a fusion category. Here we analyze the structure and representation theory of fusion rings with a basis of elements whose Frobenius-Perron dimensions take exactly one value distinct from 1. Our goal is a set of results which assist in characterizing when such fusion rings are categorifiable. As proof of concept, we completely classify the categorifiable near-group fusion rings for an infinite collection of finite abelian groups, a task that to-date has only been completed for three such groups.
