Exact factorizations and extensions of fusion categories
| Autor: | Shlomo Gelaki |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Finite group
Fusion Algebra and Number Theory Generalization 010102 general mathematics 01 natural sciences Algebra Factorization Product (mathematics) Mathematics::Category Theory 0103 physical sciences Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) 010307 mathematical physics 0101 mathematics Indecomposable module Categorical variable Mathematics |
| Popis: | 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 group-theoretical fusion category by another one, provide some examples, and propose a few natural questions. 14 pages; references added; to appear in the Journal of Algebra |
| Databáze: | OpenAIRE |
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