Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 357-387 |
| Seitenumfang | 31 |
| Fachzeitschrift | Journal of algebraic combinatorics |
| Jahrgang | 29 |
| Ausgabenummer | 3 |
| Publikationsstatus | Veröffentlicht - 1 Mai 2009 |
| Extern publiziert | Ja |
Abstract
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 ℤ/2ℤ 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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Algebra und Zahlentheorie
- Mathematik (insg.)
- Diskrete Mathematik und Kombinatorik
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in: Journal of algebraic combinatorics, Jahrgang 29, Nr. 3, 01.05.2009, S. 357-387.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Integral modular data and congruences
AU - Cuntz, Michael
PY - 2009/5/1
Y1 - 2009/5/1
N2 - 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 ℤ/2ℤ 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.
AB - 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 ℤ/2ℤ 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.
KW - Fourier matrix
KW - Fusion algebra
KW - Modular data
KW - Modular group
KW - Quantum double
UR - http://www.scopus.com/inward/record.url?scp=67349207066&partnerID=8YFLogxK
U2 - 10.1007/s10801-008-0139-y
DO - 10.1007/s10801-008-0139-y
M3 - Article
AN - SCOPUS:67349207066
VL - 29
SP - 357
EP - 387
JO - Journal of algebraic combinatorics
JF - Journal of algebraic combinatorics
SN - 0925-9899
IS - 3
ER -