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. 
1 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

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

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

Simple nuclear C*-algebras not isomorphic to their opposites

It is shown that it is consistent with Zermelo–Fraenkel set theory with the axiom of choice (ZFC) that there is a simple nuclear nonseparable C∗-algebra, which is not isomorphic to its opposite algebra.

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

Approximately Finite $C^*$-Algebras and Partial Automorphisms.

We prove that every AF-algebra is isomorphic to a crossed product of a commutative AF-algebra by a partial automorphism.

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

On C*-Diagonals

  • A. Kumjian
  • Mathematics
    Canadian Journal of Mathematics
  • 1986
Preface. The impetus for this study arose from the belief that the structure of a C*-algebra is illuminated by an understanding of the manner in which abelian subalgebras embed in it. Posed in its