Abstract. The generalized Effros-Hahn conjecture for groupoid C-algebras says that, if G is amenable, then every primitive ideal of the groupoid Calgebra C(G) is induced from a stability group. We prove that the conjecture is valid for all second countable amenable locally compact Hausdorff groupoids. Our results are a sharpening of previous work of Jean Renault and depend significantly on his ...

Quantum groupoids are a joint generalization of groupoids and quantum groups. We propose a definition of a compact quantum groupoid that is based on the theory of C *-algebras and Hilbert bimodules. The essential point is that whenever one has a tensor product over C in the theory of quantum groups, one now uses a certain tensor product over the base algebra of the quantum groupoid.

In this paper we consider deformations of an algebroid stack on an étale groupoid. We construct a differential graded Lie algebra (DGLA) which controls this deformation theory. In the case when the algebroid is a twisted form of functions we show that this DGLA is quasiisomorphic to the twist of the DGLA of Hochschild cochains on the algebra of functions on the groupoid by the characteristic cl...

The purpose of this paper is to introduce the notion of loop groupoid LG associated to a groupoid G. After studying the general properties of LG, we show how this notion provides a very natural geometric interpretation for the twisted sectors of an orbifold [7], and for the inner local systems introduced by Ruan [14] by means of a natural generalization of the concept holonomy of a gerbe.

We study the structure of the flow monoid of a regular semigroup. This arises from the approach of Nambooripad of considering a regular semigroup as a groupoid – a category in which every morphism is invertible. A flow is then a section to the source map in this groupoid, and the monoid structure of the set of all flows is determined in terms of the Green relations on the original semigroup.

k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz– Krieger type. Here we develop a theory of the fundamental groupoid of a kgraph, and relate it to the fundamental groupoid of an associated graph called the 1-skeleton. We also explore the failure, in general, of k-graphs to faithfully embed into their ...

This is a study of derivations constructed from conditionally negative type functions on groupoids which illustrates Sauvageot’s theory of noncommutative Dirichlet forms.

Daughter crystals in orientation relationship with a parent crystal are called variants. They can be created by a structural phase transition (Landau or reconstructive), by twinning or by precipitation. Internal and external classes of transformations defined from the point groups of the parent and daughter phases and from a transformation matrix allow the orientations of the distinct variants ...