Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups
Drinfeld doubles of finite subgroups of SU(2) and SU(3) are investigated in detail. Their modular data – S, T and fusion matrices – are computed explicitly, and illustrated by means of fusion graphs. This allows us to reexamine certain identities on these tensor product or fusion multiplicities unde...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2013 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2013
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149196 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups / R. Coquereaux, J. Zuber // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 53 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862747083586404352 |
|---|---|
| author | Coquereaux, R. Zuber, J. |
| author_facet | Coquereaux, R. Zuber, J. |
| citation_txt | Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups / R. Coquereaux, J. Zuber // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 53 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Drinfeld doubles of finite subgroups of SU(2) and SU(3) are investigated in detail. Their modular data – S, T and fusion matrices – are computed explicitly, and illustrated by means of fusion graphs. This allows us to reexamine certain identities on these tensor product or fusion multiplicities under conjugation of representations that had been discussed in our recent paper [J. Phys. A: Math. Theor. 44 (2011), 295208, 26 pages], proved to hold for simple and affine Lie algebras, and found to be generally wrong for finite groups. It is shown here that these identities fail also in general for Drinfeld doubles, indicating that modularity of the fusion category is not the decisive feature. Along the way, we collect many data on these Drinfeld doubles which are interesting for their own sake and maybe also in a relation with the theory of orbifolds in conformal field theory.
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| first_indexed | 2025-12-07T20:49:13Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149196 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:49:13Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Coquereaux, R. Zuber, J. 2019-02-19T18:29:32Z 2019-02-19T18:29:32Z 2013 Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups / R. Coquereaux, J. Zuber // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 53 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R50; 81T40; 20C99; 18D10 DOI: http://dx.doi.org/10.3842/SIGMA.2013.039 https://nasplib.isofts.kiev.ua/handle/123456789/149196 Drinfeld doubles of finite subgroups of SU(2) and SU(3) are investigated in detail. Their modular data – S, T and fusion matrices – are computed explicitly, and illustrated by means of fusion graphs. This allows us to reexamine certain identities on these tensor product or fusion multiplicities under conjugation of representations that had been discussed in our recent paper [J. Phys. A: Math. Theor. 44 (2011), 295208, 26 pages], proved to hold for simple and affine Lie algebras, and found to be generally wrong for finite groups. It is shown here that these identities fail also in general for Drinfeld doubles, indicating that modularity of the fusion category is not the decisive feature. Along the way, we collect many data on these Drinfeld doubles which are interesting for their own sake and maybe also in a relation with the theory of orbifolds in conformal field theory. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups Article published earlier |
| spellingShingle | Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups Coquereaux, R. Zuber, J. |
| title | Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups |
| title_full | Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups |
| title_fullStr | Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups |
| title_full_unstemmed | Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups |
| title_short | Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups |
| title_sort | drinfeld doubles for finite subgroups of su(2) and su(3) lie groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149196 |
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