# 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.

## 7 Citations

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

- Mathematics
- 2022

. 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

- MathematicsJournal of Functional Analysis
- 2019

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

- MathematicsJournal of Mathematical Analysis and Applications
- 2022

### Limit operator theory for groupoids

- MathematicsTransactions of the American Mathematical Society
- 2020

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

- Mathematics
- 2023

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…

## References

SHOWING 1-10 OF 35 REFERENCES

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

- Mathematics
- 2001

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

- MathematicsJournal of Noncommutative Geometry
- 2018

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

- Mathematics
- 2002

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

- Mathematics
- 1996

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

- MathematicsJournal 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

- 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…

### Classification of Nuclear, Simple C*-algebras

- Mathematics
- 2002

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

- Mathematics
- 2001

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

- Mathematics
- 2013

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…