Factorizable R-matrices for small quantum groups

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Tobias Ohrmann
  • Simon Lentner

Externe Organisationen

  • Universität Hamburg
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Details

OriginalspracheEnglisch
Aufsatznummer076
Seitenumfang25
FachzeitschriftSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Jahrgang13
Ausgabenummer076
PublikationsstatusVeröffentlicht - 2017

Abstract

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.

ASJC Scopus Sachgebiete

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Factorizable R-matrices for small quantum groups. / Ohrmann, Tobias; Lentner, Simon.
in: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), Jahrgang 13, Nr. 076, 076, 2017.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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KW - Quantum group

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KW - R-matrix

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