| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 5771999 | Journal of Algebra | 2017 | 14 Pages |
Abstract
We introduce and study the new notion of an exact factorization B=A
- C of a fusion category B into a product of two fusion subcategories A,CâB of B. This is a categorical generalization 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 of a fusion category B into a product of two fusion subcategories A,CâB of B. This is a categorical generalization 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Shlomo Gelaki,