Geodesic
Integral modular data and congruences
Journal of Algebraic Combinatorics, Tome 29 (2009) no. 3, pp. 357-387.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We compute all fusion algebras with symmetric rational $S$-matrix up to dimension 12. Only two of them may be used as $S$-matrices in a modular datum: the $S$-matrices of the quantum doubles of $\Bbb $Z/$2\Bbb Z$ and $S _{3}$. Almost all of them satisfy a certain congruence which has some interesting implications, for example for their degrees. We also give explicitly an infinite sequence of modular data with rational $S$- and $T$-matrices which are neither tensor products of smaller modular data nor $S$-matrices of quantum doubles of finite groups. For some sequences of finite groups (certain subdirect products of $S _{3}, D _{4}, Q _{8}, S _{4}$), we prove the rationality of the $S$-matrices of their quantum doubles.
Keywords: keywords modular data, fusion algebra, quantum double, Fourier matrix, modular group 
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     author = {Cuntz, Michael},
     title = {Integral modular data and congruences},
     journal = {Journal of Algebraic Combinatorics},
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Cuntz, Michael. Integral modular data and congruences. Journal of Algebraic Combinatorics, Tome 29 (2009) no. 3, pp. 357-387. http://geodesic.mathdoc.fr/item/JAC_2009__29_3_a1/