On some integral properties of dimensions in Isaacs fusion categories

2025/07/09 by Sebastian Burciu, Burciu, S.
Mathematics · #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2507.07329

Abstract

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 is proven for any modular fusion category. This divisibility result implies the converse direction of a Ito-Michler type result for modular fusion categories, recently established by the author.

Citations

• Structure constants for premodular categories
• The monoidal center and the character algebra

Related

• Pre-modular fusion categories of small global dimensions
• Remarks on global dimensions of fusion categories
• Frobenius-Perron Dimensions of Conjugacy Classes and an Ito-Michler-Type Result in Modular Fusion Categories
• On slightly degenerate fusion categories
• On fusion categories