On formal codegrees of fusion categories

TL;DR

This paper establishes a general result showing that the dimensions of fusion categories generate Galois-invariant ideals in the ring of algebraic integers, linking algebraic number theory with fusion category theory.

Contribution

It introduces a new theoretical framework connecting the dimensions of fusion categories with Galois invariance in algebraic integers.

Findings

Global and Frobenius-Perron dimensions generate Galois-invariant ideals

Provides a unifying algebraic number theory perspective on fusion categories

Establishes foundational results with potential applications in classification

Abstract

We prove a general result which implies that the global and Frobenius-Perron dimensions of a fusion category generate Galois invariant ideals in the ring of algebraic integers.