Measured quantum groupoids associated to proper dynamical quantum groups
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 II_1 factors. In this article, we associate to suitable dynamical quantum groups, which are a purely algebraic objects, Hopf C*-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 C*-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 SU_q(2) studied by Koelink and Rosengren.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2012
- DOI:
- 10.48550/arXiv.1206.6744
- arXiv:
- arXiv:1206.6744
- Bibcode:
- 2012arXiv1206.6744T
- Keywords:
-
- Mathematics - Operator Algebras;
- Mathematics - Quantum Algebra;
- 46L99;
- 81R50;
- 20G42;
- 16T25
- E-Print:
- revised version to appear in Journal of Noncommutative geometry