# Algebraic realization of noncommutative near-group fusion categories

## TL;DR

This paper provides an algebraic construction method for noncommutative near-group fusion categories, building on prior classifications and offering an alternative to operator algebraic approaches.

## Contribution

It introduces a purely algebraic approach to construct noncommutative near-group fusion categories from Morita equivalent pointed categories.

## Key findings

- Classified noncommutative near-group fusion categories using operator algebraic methods
- Established a purely algebraic construction method for these categories
- Connected the construction to pointed categories via Morita equivalence

## Abstract

Noncommutative near-group fusion categories were completely classified in the previous work of the first named author by using an operator algebraic method (and hence under the assumption of unitarity), and they were shown to be group theoretical though the corresponding pointed categories were not identified. In this note we give a purely algebraic construction of the noncommutative near-group fusion categories starting from pointed categories categorically Morita equivalent to them.