Fourier matrices of small rank
DOI:
https://doi.org/10.13069/jacodesmath.369865Keywords:
Fourier matrices, Modular data, Fusion rings, $C$-algebrasAbstract
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.
Received: 6 May 2017 | Accepted: 27 October 2017
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