Measured Quantum Groupoids Associated with Matched Pairs of Locally Compact Groupoids
نویسنده
چکیده
Generalizing the notion of matched pair of groups, we define and study matched pairs of locally compact groupoids endowed with Haar systems, in order to give new examples of measured quantum groupoids.
منابع مشابه
Outer Actions of Measured Quantum Groupoids
Mimicking a recent article of Stefaan Vaes, in which was proved that every locally compact quantum group can act outerly, we prove that we get the same result for measured quantum groupoids, with an appropriate definition of outer actions of measured quantum groupoids. This result is used to show that every measured quantum groupoid can be found from some depth 2 inclusion of von Neumann algebras.
متن کاملRelative Matched Pairs of Finite Groups from Depth Two Inclusions of Von Neumann Algebras to Quantum Groupoids
In this work we give a generalization of matched pairs of (finite) groups to describe a general class of depth two inclusions of factor von Neumann algebras and the C*-quantum groupoids associated with, using double groupoids. Date: Preliminary version of the 03/27/07. 1991 Mathematics Subject Classification. (2000) 46L37, 20L05, 20G42, 20 99.
متن کاملMeasured Quantum Groupoids with a Central Basis
In ([L2]), Franck Lesieur had introduced a notion of measured quantum groupoid, in the setting of von Neumann algebras. In an annex of [E6], Lesieur’s axioms have been simplified. In this article, we suppose that the basis is central; in that case, we prove that a specific sub-C∗ algebra is, in a sense, invariant under all the data which define the measured quantum group, which allow us to prov...
متن کاملCompact quantum groupoids in the setting of C -algebras
We propose a definition of compact quantum groupoids in the setting of C -algebras, associate to such a quantum groupoid a regular C -pseudo-multiplicative unitary, and use this unitary to construct a dual Hopf C -bimodule and to pass to a measurable quantum groupoid in the sense of Enock and Lesieur. Moreover, we discuss examples related to compact and to étale groupoids and study principal co...
متن کاملRepresentations of Matched Pairs of Groupoids and Applications to Weak Hopf Algebras
Abstract. We introduce the category of set-theoretic representations of a matched pair of groupoids. This is a monoidal category endowed with a monoidal functor fl to the category of quivers over the common base of the groupoids in the matched pair. We study monoidal functors between two such categories of representations which preserve the functor fl. We show that the centralizer of such a mon...
متن کامل