Groupoid -algebras.
Groupoids and compact quantum groups
Higher-dimensional algebra. V: 2-Groups.
Isomorphic groupoid -algebras associated with different Haar systems.
La dynamique des pseudogroupes de rotations.
Layer potentials C*-algebras of domains with conical points
To a domain with conical points Ω, we associate a natural C*-algebra that is motivated by the study of boundary value problems on Ω, especially using the method of layer potentials. In two dimensions, we allow Ω to be a domain with ramified cracks. We construct an explicit groupoid associated to ∂Ω and use the theory of pseudodifferential operators on groupoids and its representations to obtain our layer potentials C*-algebra. We study its structure, compute the associated K-groups, and prove Fredholm...
Lie groupoids of mappings taking values in a Lie groupoid
Endowing differentiable functions from a compact manifold to a Lie group with the pointwise group operations one obtains the so-called current groups and, as a special case, loop groups. These are prime examples of infinite-dimensional Lie groups modelled on locally convex spaces. In the present paper, we generalise this construction and show that differentiable mappings on a compact manifold (possibly with boundary) with values in a Lie groupoid form infinite-dimensional Lie groupoids which we...
Local and nice structures of the groupoid of an equivalence relation
Measured quantum groupoids associated with matched pairs of locally compact groupoids
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.
Morita equivalence and symplectic realizations of Poisson manifolds
Non-Hausdorff groupoids, proper actions and -theory.
On Lie algebroid actions and morphisms
On the existence of a Haar measure in topological IP-loops
In this paper, we give conditions ensuring the existence of a Haar measure in topological IP-loops.
On the linearization theorem for proper Lie groupoids
We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the fixed point case (known as Zung’s theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passage to general orbits (Weinstein) is given a more conceptual interpretation: as a manifestation of Morita invariance. We also clarify the precise statements of the Linearization Theorem (there has been some confusion on this, which has propagated throughout...
Orbit projections of proper Lie groupoids as fibrations
Let be a source locally trivial proper Lie groupoid such that each orbit is of finite type. The orbit projection is a fibration if and only if is regular.
Poznámka o -triedách v komutatívných Hausdorffových bikompaktních pologrupách
Principal fibre bundles with structural Lie groupoid.
Proper groupoids and momentum maps : linearization, affinity, and convexity
Pseudodifferential analysis on continuous family groupoids.
Representations of étale Lie groupoids and modules over Hopf algebroids
The classical Serre-Swan's theorem defines an equivalence between the category of vector bundles and the category of finitely generated projective modules over the algebra of continuous functions on some compact Hausdorff topological space. We extend these results to obtain a correspondence between the category of representations of an étale Lie groupoid and the category of modules over its Hopf algebroid that are of finite type and of constant rank. Both of these constructions are functorially...