Fourier matrices of small rank

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.2010 MSC: 05E30, 05E99, 81R05

Diagonal torsion matrices associated with modular data

“…If an s-matrix has integral entries then the s-matrix is called integral Fourier matrix and the pair (s, T ) is called an integral modular datum, see [2,Definition 3.1]. A Fourier matrix S is called a homogeneous Fourier matrix if all the entries of first row of its associated s-matrix are equal to 1, otherwise, S is called a non-homogenous Fourier matrix, see [5] and [6]. Let (S, T ) and (S 0 , T 0 ) be two modular data.…”

“…In particular, it has nice applications to string theory, statistical mechanics, and condensed matter physics, see [4] and [7]. Modular data give rise to fusion rings, C-algebras and C * -algebras, see [2], [3], [5] and [6]. These rings and algebras are interesting topics of study in their own right.…”