Exact factorizations and extensions of fusion categories

JOURNAL OF ALGEBRA

卷:480

Article

Gelaki, Shlomo¹ 

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

关键词: Fusion categories;    Module categories;    Exact sequences of fusion categories;    Exact factorizations of fusion categories;   

DOI  :  10.1016/j.jalgebra.2017.02.034

来源: Elsevier

【 摘 要 】

We introduce and study the new notion of an exact factorization B = A . C of a fusion category into a product of two fusion subcategories A, C subset of B of B. This is a categorical goneraifration of the well known notion of an exact factorization of a finite group into a product of two subgroups. We then relate exact factorizations of fusion categories to exact sequences of fusion categories with respect to an indecomposable module category, which was introduced and studied in [7]. We also apply our results to study extensions of a group-theoretical fusion category by another one, provide some examples, and propose a few natural questions. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free