Classification of homogeneous Fourier matrices

Abstract

Modular data are commonly studied in mathematics and physics. A modular datum defines a finite-dimensional representation of the modular group \(SL_2(\mathbb{Z})\). In this paper, we show that there is a one-to-one correspondence between  Fourier matrices associated to modular data and self-dual \(C\)-algebras that satisfy a certain condition. We prove that a homogenous \(C\)-algebra arising from a Fourier matrix has all the degrees equal to \(1\).