Integral modular data and congruences
| dc.creator | Cuntz, Michael | |
| dc.date | 2006-11-08 | |
| dc.date | 2008-06-03 | |
| dc.date.accessioned | 2026-07-07T09:42:17Z | |
| dc.date.available | 2026-07-07T09:42:17Z | |
| dc.description | 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 $\mathbb{Z}/2\mathbb{Z}$ 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. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611233 | |
| dc.identifier | http://arxiv.org/abs/math/0611233 | |
| dc.identifier | doi:10.1007/s10801-008-0139-y | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162125 | |
| dc.subject | Representation Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 81R05; 16S99; 19A49; 20C40 | |
| dc.title | Integral modular data and congruences | |
| dc.type | text |