Fourier matrices of small rank

Year 2018, Volume: 5 Issue: 2, 51 - 63, 29.05.2018

Gurmail Singh

https://doi.org/10.13069/jacodesmath.369865

Cited By: 1

Abstract

Modular data is an important topic of study in rational conformal field theory.
Cuntz, using a computer, classified the Fourier matrices associated to modular data with rational entries up to rank $12$, see [3].
Here we use the properties of $C$-algebras arising from Fourier matrices to classify complex Fourier matrices under certain conditions up to rank $5$. Also, we establish some results that are helpful in recognizing $C$-algebras that not arising from Fourier matrices by just looking at the first row of their character tables.

Keywords

Fourier matrices, Modular data, Fusion rings, C-algebras

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