Measured quantum transformation groupoids

Enock M., Timmermann T.

Abstract

In this article, whenGis a locally compact quantum group, we associate, to a braidedcommutative G-Yetter-Drinfel'd algebra .N; a;ba/ equipped with a normal faithful semi-finite weight verifying some appropriate condition (in particular if it is invariant with respect to a, or toba), a structure of a measured quantum groupoid. The dual structure is then given by .N;ba; a/. Examples are given, especially the situation of a quotient type co-ideal of a compact quantum group. This construction generalizes the standard construction of a transformation groupoid. Most of the results were announced by the second author in 2011, at a conference in Warsaw.