Opposite algebras of groupoid C*-algebras

@article{Buss2017OppositeAO,
  title={Opposite algebras of groupoid C*-algebras},
  author={Alcides Buss and Aidan Sims},
  journal={Israel Journal of Mathematics},
  year={2017},
  volume={244},
  pages={759 - 774}
}
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 isomorphic to twisted groupoid C*-algebras. We also prove that the opposite algebra of a section algebra of a Fell bundle over a groupoid is isomorphic to the section algebra of a natural opposite bundle. 
View on Springer
arxiv.org
7 Citations
Highly Influential Citations
1
Background Citations
2

7 Citations

Alexandrov groupoids and the nuclear dimension of twisted groupoid $\mathrm{C}^*$-algebras

. We consider a twist E over an ´etale groupoid G . When G is principal, we prove that the nuclear dimension of the reduced twisted groupoid C ∗ -algebra is bounded by a number depending on the…

Inverse systems of groupoids, with applications to groupoid C⁎-algebras

Renault's j-map for Fell bundle C⁎-algebras

Limit operator theory for groupoids

We extend the symbol calculus and study the limit operator theory for σ \sigma -compact, étale, and amenable groupoids, in the Hilbert space case. This approach not only unifies various…

Banach algebras associated to twisted \'etale groupoids: inverse semigroup disintegration and representations on $L^p$-spaces

We initiate a study of (real or complex) Banach algebras associated to twisted \'etale groupoids $(\mathcal{G},\mathcal{L})$ and to twisted inverse semigroup actions, which provides a general…

A Cuntz-Pimsner model for the C⁎-algebra of a graph of groups

Poincaré duality for Cuntz–Pimsner algebras

References

SHOWING 1-10 OF 35 REFERENCES

CONTINUOUS–TRACE C*-ALGEBRAS NOT ISOMORPHIC TO THEIR OPPOSITE ALGEBRAS

We give examples of locally trivial continuous-trace C*-algebra not isomorphic to their opposite algebras. Our examples include a unital C*-algebra which is both stably isomorphic to and homotopy…

Simple nuclear C*-algebras not equivariantly isomorphic to their opposites

We exhibit examples of simple separable nuclear C*-algebras, along with actions of the circle group and outer actions of the integers, which are not equivariantly isomorphic to their opposite…

A simple separable C*-algebra not isomorphic to its opposite algebra

We give an example of a simple separable C*-algebra that is not isomorphic to its opposite algebra. Our example is nonnuclear and stably finite, has real rank zero and stable rank one, and has a…

Fell bundles over groupoids

We study the C*-algebras associated to Fell bundles over groupoids and give a notion of equivalence for Fell bundles which guarantees that the associated C*-algebras are strong Morita equivalent. As…

Continuous trace C*-algebras with given Dixmer-Douady class

  • I. RaeburnJoseph L. Taylor
  • Mathematics
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
  • 1985
Abstract We give an explicit construction of a continuous trace C*algebra with prescribed Dixmier-Douady class, and with only finite-dimensional irreducible representations. These algebras often have…

Cartan Subalgebras in $C^*$-Algebras

  • J. Renault
  • Mathematics
    Irish 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…

A Dixmier-Douady theorem for Fell algebras

Classification of Nuclear, Simple C*-algebras

The possibility that nuclear (or amenable) C*-algebras should be classified up to isomorphism by their K-theory and related invariants was raised in an article by Elliott [48] (written in 1989) in…

Classification of Nuclear C*-Algebras. Entropy in Operator Algebras

I. Classification of Nuclear, Simple C*-algebras.- II. A Survey of Noncommutative Dynamical Entropy.

A simple separable exact C*-algebra not anti-isomorphic to itself

We give an example of an exact, stably finite, simple, separable C*-algebra D which is not isomorphic to its opposite algebra. Moreover, D has the following additional properties. It is stably…