22 Citations
Fell algebras, groupoids, and projections
- Mathematics
- 2021
Examples of Fell algebras with compact spectrum and trivial DixmierDouady invariant are constructed to illustrate differences with the case of continuoustrace C∗-algebras. At the level of the…
Reconstruction of twisted Steinberg algebras
- Mathematics
- 2021
We show how to recover a discrete twist over an ample Hausdorff groupoid from a pair consisting of an algebra and what we call a quasi-Cartan subalgebra. We identify precisely which twists arise in…
Simplicity of twisted C*-algebras of Deaconu--Renault groupoids
- Mathematics
- 2021
We consider Deaconu–Renault groupoids associated to actions of finite-rank free abelian monoids by local homeomorphisms of locally compact Hausdorff spaces. We study simplicity of the twisted…
CARTAN SUBALGEBRAS IN C∗-ALGEBRAS OF HAUSDORFF
- Mathematics
- 2016
The reduced C∗-algebra of the interior of the isotropy in any Hausdorff étale groupoid G embeds as a C∗-subalgebra M of the reduced C∗-algebra of G. We prove that the set of pure states of M with…
Cartan Subalgebras in C*-Algebras of Haus dorff étale Groupoids
- MathematicsIntegral Equations and Operator Theory
- 2016
The reduced C*-algebra of the interior of the isotropy in any Hausdorff étale groupoid G embeds as a C*-subalgebra M of the reduced C*-algebra of G. We prove that the set of pure states of M with…
Cartan Subalgebras in C*-Algebras of Haus dorff étale Groupoids
- Mathematics
- 2016
The reduced C*-algebra of the interior of the isotropy in any Hausdorff étale groupoid G embeds as a C*-subalgebra M of the reduced C*-algebra of G. We prove that the set of pure states of M with…
The stable algebra of a Wieler solenoid: inductive limits and $K$ -theory
- MathematicsErgodic Theory and Dynamical Systems
- 2020
Wieler has shown that every irreducible Smale space with totally disconnected stable sets is a solenoid (i.e., obtained via a stationary inverse limit construction). Using her construction, we show…
Opposite algebras of groupoid C*-algebras
- MathematicsIsrael Journal of Mathematics
- 2021
We show that every groupoid C*-algebra is isomorphic to its opposite, and deduce that there exist C*-algebras that are not stably isomorphic to groupoid C*-algebras, though many of them are stably…
Topological freeness for C⁎-correspondences
- MathematicsJournal of Mathematical Analysis and Applications
- 2019
K-theory and homotopies of 2-cocycles on higher-rank graphs
- Mathematics
- 2015
This paper continues our investigation into the question of when a homotopy of 2-cocycles on a locally compact Hausdorff groupoid gives rise to an isomorphism of the K-theory groups of the twisted…
References
SHOWING 1-10 OF 58 REFERENCES
Cartan Subalgebras in $C^*$-Algebras
- MathematicsIrish Mathematical Society Bulletin
- 2008
According to J. Feldman and C. Moore's well- known theorem on Cartan subalgebras, a variant of the group measure space construction gives an equivalence of categories between twisted countable…
Dixmier-Douady Classes of Dynamical Systems and Crossed Products
- MathematicsCanadian Journal of Mathematics
- 1993
Abstract Continuous-trace C*-algebras A with spectrum T can be characterized as those algebras which are locally Monta equivalent to C0(T). The Dixmier-Douady class δ(A) is an element of the Čech…
Nonassociative Tori and Applications to T-Duality
- Mathematics
- 2006
In this paper, we initiate the study of C*-algebras endowed with a twisted action of a locally compact abelian Lie group , and we construct a twisted crossed product , which is in general a…
Non-Hausdorff étale groupoids
- Mathematics
- 2011
We present examples of non-Hausdorff, etale, essentially principal groupoids for which three results, known to hold in the Hausdorff case, fail. These results are: (A) the subalgebra of continuous…
Extensions of Pure States and Projections of Norm One
- Mathematics
- 1999
Abstract We show that the extension property for pure states of a C *-subalgebra B of a C *-algebra A leads to the existence of a projection of norm one R : A → B in the case where B is liminal with…
Non-Hausdorff groupoids
- Mathematics
- 2008
We present examples of non-Hausdorff, etale, essentially principal groupoids for which three results, known to hold in the Hausdorff case, fail. These results are: (A) the subalgebra of continuous…
Automorphisms of Certain Simple C*-algebras
- Mathematics
- 1980
It has been observed by M. Takesaki (private communication) that for the C*-algebras 0 n there is a bijective correspondence between unitaries in 0 n and endomorphisms that leave the unit fixed. We…
Morita Equivalence and Continuous-Trace $C^*$-Algebras
- Mathematics
- 1998
The algebra of compact operators Hilbert $C^*$-modules Morita equivalence Sheaves, cohomology, and bundles Continuous-trace $C^*$-algebras Applications Epilogue: The Brauer group and group actions…
Diagonals in algebras of continuous trace
- Mathematics
- 1985
In the following the notion of diagonal (cf. [7], [14]) is studied under the restr ict ion that the ambient algebra be of continuous trace. In a sense this study may be viewed as a sequel to [6], as…
Operator Algebras
- Mathematics
- 1998
p. 2 I.1.1.4: The Riesz-Fischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e}. If…