Exact factorizations and extensions of fusion categories
Abstract
We introduce and study the new notion of an {\em exact factorization} $\mathcal{B}=\mathcal{A}\bullet \mathcal{C}$ of a fusion category $\mathcal{B}$ into a product of two fusion subcategories $\mathcal{A},\mathcal{C}\subseteq \mathcal{B}$ of $\mathcal{B}$. 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 by P. Etingof and the author in \cite{EG}. We also apply our results to study extensions of a grouptheoretical fusion category by another one, provide some examples, and propose a few natural questions.
 Publication:

arXiv eprints
 Pub Date:
 March 2016
 arXiv:
 arXiv:1603.01568
 Bibcode:
 2016arXiv160301568G
 Keywords:

 Mathematics  Quantum Algebra
 EPrint:
 14 pages