Related papers: Some examples of factor groupoids
We compute explicitly the K-groups of some boundary groupoid C*-algebras with exponential isotropy subgroups. Then we derive index formulas that computes the K-theoretic and Fredholm indexes of elliptic (respectively totally elliptic)…
We give a concise introduction to (discrete) algebras arising from \'etale groupoids, (aka Steinberg algebras) and describe their close relationship with groupoid C*-algebras. Their connection to partial group rings via inverse semigroups…
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…
We construct a large class of morphisms, which we call partial morphisms, of groupoids that induce $*$-morphisms of maximal and minimal groupoid $C^*$-algebras. We show that the association of a groupoid to its maximal (minimal) groupoid…
We describe a construction for the full C$^*$-algebra of a possibly unsaturated Fell bundle over a possibly non-Hausdorff locally compact \'etale groupoid without appealing to Renault's disintegration theorem. This construction generalises…
We present a new method, involving monads and comonads from category theory, to help establish a certain type of equivalence of subcategories. As a case study we consider the category of topological gradings of $C^*$-algebras over a fixed…
The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras…
We give the first examples of \'etale (non-Hausdorff) groupoids $\mathcal G$ whose $C^*$-algebras contain singular elements that cannot be approximated by singular elements in $\mathcal C_c(\mathcal G)$. We provide two examples: one is a…
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…
We introduce and investigate using Hilbert modules the properties of the {\em Fourier algebra} $A(G)$ for a locally compact groupoid $G$. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This…
Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce…
In this paper, we introduce properties including groupoid comparison, pure infiniteness and paradoxical comparison as well as a new algebraic tool called groupoid semigroup for locally compact Hausdorff \'{e}tale groupoids. We show these…
Given a pair of dynamical systems we consider a pair of commuting von Neumann factors of type 11_1. The construction is a generalization of classical von Neumann-Murrey and grouppoid construction. It gives a natural examples of factors with…
This is Part II in our multi-part series of papers developing the theory of a subclass of locally compact quantum groupoids ("quantum groupoids of separable type"), based on the purely algebraic notion of weak multiplier Hopf algebras. The…
We introduce and investigate using Hilbert modules the properties of the Fourier algebra A(G) for a locally compact groupoid G. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This includes as a…
Two conjectures about homology groups, K-groups and topological full groups of minimal etale groupoids on Cantor sets are formulated. We verify these conjectures for many examples of etale groupoids including products of etale groupoids…
This is a continuation of our previous paper studying the structure of Cartan subalgebras of von Neumann factors of type II_1. We provide more examples of II_1 factors having either zero, one or several Cartan subalgebras. We also prove a…
The category $\cal{C}$ (studied by Andersen-Jantzen-Soergel) of representations of a Lusztig's small quantum group at a root of unity, together with its modular structure, is defined geometrically, using configuration spaces.
We develop a framework suitable for obtaining simplicity criteria for reduced $C^*$-algebras of Hausdorff etale groupoids. This is based on the study of certain non-degenerate $C^*$-subalgebras (in the case of groupoids, the $C^*$-algebra…
We consider the homology theory of \'etale groupoids introduced by Crainic and Moerdijk, with particular interest to groupoids arising from topological dynamical systems. We prove a K\"unneth formula for products of groupoids and a…