Details
| Original language | English |
|---|---|
| Pages (from-to) | 357-387 |
| Number of pages | 31 |
| Journal | Journal of algebraic combinatorics |
| Volume | 29 |
| Issue number | 3 |
| Publication status | Published - 1 May 2009 |
| Externally published | Yes |
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.
Keywords
- Fourier matrix, Fusion algebra, Modular data, Modular group, Quantum double
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Discrete Mathematics and Combinatorics
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In: Journal of algebraic combinatorics, Vol. 29, No. 3, 01.05.2009, p. 357-387.
Research output: Contribution to journal › Article › Research › 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 -