… In the next section, we give preliminaries about groupoids, groupoid actions, skew
groupoid rings, weak bialgebras, groupoid gradings, groupoid coactions, and weak smash …

… This really extends Takesaki duality for group actions [T2], [NT]. In § … duality for integrable
coactions of measured groupoids. At this point, the author has been unable to show the duality …

… originated from a more careful observation of the groupoid von Neumann algebra of a general
measured groupoid. Before I explain what I mean by actions and coactions of groupoids, I …

… on a crossed product groupoid for a G-action on a generalized … We also describe group
actions on the groupoids that make the … groupoids appear in the statement of classical T-duality. …

… concepts of actions and coactions of finite groupoids. Then a … expect a duality type theorem
between actions and coactions. … never obtain a duality type theorem in the groupoid case, as …

… actions, principal bundles, and bibundles of higher groupoids. Roughly, we use Kan fibrations
to model actions of higher groupoids; … principal bundles of higher groupoids; we use inner …

… by actions and coactions of measured groupoids, we think that it is better to mention the history
of groupoid actions on … A notion of an action of a measured groupoid on a von Neumann …

… groupoid algebra of a measured groupoid. In §2, we study the "Plancherel weight" of a measured
groupoid … [Yl] Yamanouchi, T., Duality for actions and coactions of measured groupoids …

… of certain action groupoids, which decode the dynamical system. Similarly, we show that
cohomology classes of action groupoids associated to dynamical systems can be viewed as co…

… G is minimal, ie, if all its orbits are dense, then we can choose any point x ∈ X, and define
the dual groupoid G⊤ as the groupoid of germs of the action on ∂Gx of the asymptotic …