3 papers
math.QA2025
Burnside type results for fusion categories
Sebastian Burciu, Sebastien Palcoux
In this paper, we extend a classical vanishing result of Burnside from the character tables of finite groups to the character tables of commutative fusion rings, or more generally…
math.QA2025
On some integral properties of dimensions in Isaacs fusion categories
S. Burciu
For a fusion category, we prove some new integral properties concerning the dimension of a simple object that generates a Isaacs fusion subcategory. A stronger divisibility result…
math.QA2024
Frobenius-Perron Dimensions of Conjugacy Classes and an Ito-Michler-Type Result in Modular Fusion Categories
S. Burciu
The influence of certain arithmetic conditions on the sizes of conjugacy classes of a finite group on the group structure has been extensively studied in recent years. In this pape…