JournalsjncgVol. 9, No. 1pp. 35–82

Measured quantum groupoids associated to proper dynamical quantum groups

  • Thomas Timmermann

    Westfälische Wilhelms-Universität Münster, Germany
Measured quantum groupoids associated to proper dynamical quantum groups cover
Download PDF

Abstract

Dynamical quantum groups were introduced by Etingof and Varchenko in connection with the dynamical quantum Yang–Baxter equation, and measured quantum groupoids were introduced by Enock, Lesieur and Vallin in their study of inclusions of type II1_1 factors. In this article, we associate to suitable dynamical quantum groups, which are purely algebraic objects, Hopf CC*-bimodules and measured quantum groupoids on the level of von Neumann algebras. Assuming invariant integrals on the dynamical quantum group, we first construct a fundamental unitary which yields Hopf bimodules on the level of CC*-algebras and von Neumann algebras. Next, we assume properness of the dynamical quantum group and lift the integrals to the operator algebras. In a subsequent article, this construction shall be applied to the dynamical SUq_q(2) studied by Koelink and Rosengren.

Cite this article

Thomas Timmermann, Measured quantum groupoids associated to proper dynamical quantum groups. J. Noncommut. Geom. 9 (2015), no. 1, pp. 35–82

DOI 10.4171/JNCG/187