Factorizable R-Matrices for Small Quantum Groups
Representations of small quantum groups uq(g) at a root of unity and their extensions provide interesting tensor categories, that appear in different areas of algebra and mathematical physics. There is an ansatz by Lusztig to endow these categories with the structure of a braided tensor category. In...
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| Datum: | 2017 |
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| Sprache: | English |
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Інститут математики НАН України
2017
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/148764 |
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| Zitieren: | Factorizable R-Matrices for Small Quantum Groups / S. Lentner, T. Ohrmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 19 назв. — англ. |
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irk-123456789-1487642019-02-19T01:23:49Z Factorizable R-Matrices for Small Quantum Groups Lentner, S. Ohrmann, T. Representations of small quantum groups uq(g) at a root of unity and their extensions provide interesting tensor categories, that appear in different areas of algebra and mathematical physics. There is an ansatz by Lusztig to endow these categories with the structure of a braided tensor category. In this article we determine all solutions to this ansatz that lead to a non-degenerate braiding. Particularly interesting are cases where the order of q has common divisors with root lengths. In this way we produce familiar and unfamiliar series of (non-semisimple) modular tensor categories. In the degenerate cases we determine the group of so-called transparent objects for further use. 2017 Article Factorizable R-Matrices for Small Quantum Groups / S. Lentner, T. Ohrmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 19 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B37; 20G42; 81R50; 18D10 DOI:10.3842/SIGMA.2017.076 http://dspace.nbuv.gov.ua/handle/123456789/148764 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Representations of small quantum groups uq(g) at a root of unity and their extensions provide interesting tensor categories, that appear in different areas of algebra and mathematical physics. There is an ansatz by Lusztig to endow these categories with the structure of a braided tensor category. In this article we determine all solutions to this ansatz that lead to a non-degenerate braiding. Particularly interesting are cases where the order of q has common divisors with root lengths. In this way we produce familiar and unfamiliar series of (non-semisimple) modular tensor categories. In the degenerate cases we determine the group of so-called transparent objects for further use. |
| format |
Article |
| author |
Lentner, S. Ohrmann, T. |
| spellingShingle |
Lentner, S. Ohrmann, T. Factorizable R-Matrices for Small Quantum Groups Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Lentner, S. Ohrmann, T. |
| author_sort |
Lentner, S. |
| title |
Factorizable R-Matrices for Small Quantum Groups |
| title_short |
Factorizable R-Matrices for Small Quantum Groups |
| title_full |
Factorizable R-Matrices for Small Quantum Groups |
| title_fullStr |
Factorizable R-Matrices for Small Quantum Groups |
| title_full_unstemmed |
Factorizable R-Matrices for Small Quantum Groups |
| title_sort |
factorizable r-matrices for small quantum groups |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148764 |
| citation_txt |
Factorizable R-Matrices for Small Quantum Groups / S. Lentner, T. Ohrmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 19 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT lentners factorizablermatricesforsmallquantumgroups AT ohrmannt factorizablermatricesforsmallquantumgroups |
| first_indexed |
2025-07-12T20:12:21Z |
| last_indexed |
2025-07-12T20:12:21Z |
| _version_ |
1837473351811989504 |