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Factorizable R-Matrices for Small Quantum Groups
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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Factorizable R-Matrices for Small Quantum Groups
Інший ID:
2010 Mathematics Subject Classification: 17B37; 20G42; 81R50; 18D10
DOI:10.3842/SIGMA.2017.076
DOI:10.3842/SIGMA.2017.076
Посилання:
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.
Підтримка:
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.
Дата:
2017
Переглядів:
700
Завантажень:
264
Анотація:
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.
