Irrational braided generalized near-groups

TL;DR

This paper classifies certain complex algebraic structures called braided generalized near-group fusion categories with non-integer global dimension, identifying exactly two such categories up to equivalence.

Contribution

It provides a complete classification of non-integer global dimension braided generalized near-group fusion categories, revealing their limited variety.

Findings

Exactly two such categories exist up to equivalence.

Classification is achieved through analysis of their algebraic properties.

Results contribute to understanding the structure of fusion categories.

Abstract

We classify braided generalized near-group fusion categories whose global dimension is not an integer; there are exactly two up to Grothendieck equivalence and taking products with braided pointed fusion categories.