|
This article is cited in 9 scientific papers (total in 9 papers)
Factorizable $R$-Matrices for Small Quantum Groups
Simon Lentner, Tobias Ohrmann Fachbereich Mathematik, University of Hamburg, Bundesstraße 55, 20146 Hamburg, Germany
Abstract:
Representations of small quantum groups $u_q({\mathfrak{g}})$ 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.
Keywords:
factorizable; $R$-matrix; quantum group; modular tensor category; transparent object.
Received: January 16, 2017; in final form September 15, 2017; Published online September 25, 2017
Citation:
Simon Lentner, Tobias Ohrmann, “Factorizable $R$-Matrices for Small Quantum Groups”, SIGMA, 13 (2017), 076, 25 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1276 https://www.mathnet.ru/eng/sigma/v13/p76
|
Statistics & downloads: |
Abstract page: | 205 | Full-text PDF : | 29 | References: | 25 |
|