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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2017 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2017
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148764 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-148764 |
|---|---|
| record_format |
dspace |
| spelling |
Lentner, S. Ohrmann, T. 2019-02-18T18:47:57Z 2019-02-18T18:47:57Z 2017 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 https://nasplib.isofts.kiev.ua/handle/123456789/148764 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. Both authors thank Christoph Schweigert for helpful discussions and support. They also thank the referees, who gave a relevant contribution to improve the article with their comments. The first author was supported by the DAAD P.R.I.M.E program funded by the German BMBF and the EU Marie Curie Actions as well as the Graduiertenkolleg RTG 1670 at the University of Hamburg. The second author was supported by the Collaborative Research Center SFB 676 at the University of Hamburg. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Factorizable R-Matrices for Small Quantum Groups Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Factorizable R-Matrices for Small Quantum Groups |
| spellingShingle |
Factorizable R-Matrices for Small Quantum Groups Lentner, S. Ohrmann, T. |
| 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 |
| author |
Lentner, S. Ohrmann, T. |
| author_facet |
Lentner, S. Ohrmann, T. |
| publishDate |
2017 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.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. |
| work_keys_str_mv |
AT lentners factorizablermatricesforsmallquantumgroups AT ohrmannt factorizablermatricesforsmallquantumgroups |
| first_indexed |
2025-12-07T16:50:27Z |
| last_indexed |
2025-12-07T16:50:27Z |
| _version_ |
1850868999374503936 |