Some properties of group-theoretical categories

被引：17

作者：

Gelaki, Shlomo ^{[1
]}

Naidu, Deepak ^{[2
]}

机构：

[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

[2] Univ New Hampshire, Dept Math & Stat, Durham, NH 03824 USA

来源：

JOURNAL OF ALGEBRA | 2009年 / 322卷 / 08期

基金：

以色列科学基金会;

关键词：

Fusion categories; Group-theoretical categories; FUSION CATEGORIES; MODULE CATEGORIES; HOPF-ALGEBRAS;

D O I：

10.1016/j.jalgebra.2009.05.047

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We first show that every group-theoretical category is graded by a certain double coset ring. As a consequence, we obtain a necessary and sufficient condition for a group-theoretical category to be nilpotent. We then give an explicit description of the simple objects in a group-theoretical category (following [O2]) and of the group of invertible objects of a group-theoretical category, in group-theoretical terms. Finally, under certain restrictive conditions, we describe the universal grading group of a group-theoretical category. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：2631 / 2641

页数：11

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