Reduced twisted crossed products over C*-simple groups

@article{Bryder2016ReducedTC,
  title={Reduced twisted crossed products over C*-simple groups},
  author={Rasmus Sylvester Bryder and Matthew Kennedy},
  journal={arXiv: Operator Algebras},
  year={2016}
}
We consider reduced crossed products of twisted C*-dynamical systems over C*-simple groups. We prove there is a bijective correspondence between maximal ideals of the reduced crossed product and maximal invariant ideals of the underlying C*-algebra, and a bijective correspondence between tracial states on the reduced crossed product and invariant tracial states on the underlying C*-algebra. In particular, the reduced crossed product is simple if and only if the underlying C*-algebra has no… 
On reduced twisted group C*-algebras that are simple and/or have a unique trace
We study the problem of determining when the reduced twisted group C*-algebra associated with a discrete group G is simple and/or has a unique tracial state, and present new sufficient conditions for
Noncommutative boundaries and the ideal structure of reduced crossed products
A C*-dynamical system is said to have the ideal separation property if every ideal in the corresponding crossed product arises from an invariant ideal in the C*-algebra. In this paper we characterize
Simplicity and tracial weights on non-unital reduced crossed products
We extend theorems of Breuillard–Kalantar–Kennedy–Ozawa on unital reduced crossed products to the non-unital case under mild assumptions. As a result simplicity of C∗-algebras is stable under taking
A generalized powers averaging property for commutative crossed products
We prove a generalized version of Powers’ averaging property that characterizes simplicity of reduced crossed products C(X) ⋊λ G, where G is a countable discrete group, and X is a compact Hausdorff
C*-irreducibility for reduced twisted group C*-algebras
. We study C ∗ -irreducibility of inclusions of reduced twisted group C ∗ -algebras and of reduced group C ∗ -algebras. We characterize C ∗ -irreducibility in the case of an inclusion arising from a
An intrinsic characterization of C*-simplicity
  • M. Kennedy
  • Mathematics
    Annales scientifiques de l'École normale supérieure
  • 2020
A group is said to be C*-simple if its reduced C*-algebra is simple. We establish an intrinsic (group-theoretic) characterization of groups with this property. Specifically, we prove that a discrete
Characterizations of C*-simplicity
We characterize discrete groups that are C*-simple, meaning that their reduced C*-algebra is simple. First, we prove that a discrete group is C*-simple if and only if it has Powers' averaging
The ideal intersection property for essential groupoid C*-algebras
We characterise, in several complementary ways, étale groupoids with locally compact Hausdorff space of units whose essential groupoid C∗-algebra has the ideal intersection property, assuming that
...
...

References

SHOWING 1-10 OF 30 REFERENCES
Twisted crossed products of C*-algebras
  • J. Packer, I. Raeburn
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1989
Group algebras and crossed products have always played an important role in the theory of C*-algebras, and there has also been considerable interest in various twisted analogues, where the
On simplicity of reduced C*-algebras of groups
A countable group is C*-simple if its reduced C*-algebra is a simple algebra. Since Powers recognised in 1975 that non-abelian free groups are C*-simple, large classes of C*-simple groups which
The ideal structure of reduced crossed products
Let (A, G) be a C*-dynamical system with G discrete. In this paper we in- vestigate the ideal structure of the reduced crossed product C*-algebra and in particular we determine sufficient—and in some
C*-simplicity and the unique trace property for discrete groups
A discrete group is said to be C*-simple if its reduced C*-algebra is simple, and is said to have the unique trace property if its reduced C*-algebra has a unique tracial state. A dynamical
Boundaries of reduced C*-algebras of discrete groups
For a discrete group G, we consider the minimal C*-subalgebra of $\ell^\infty(G)$ that arises as the image of a unital positive G-equivariant projection. This algebra always exists and is unique up
Crossed products, the Mackey-Rieffel-Green machine and applications
We give an introduction into the ideal structure and representation theory of crossed products by actions of locally compact groups on C*-algebras. In particular, we discuss the Mackey-Rieffel-Green
A New Look at C∗-Simplicity and the Unique Trace Property of a Group
We characterize when the reduced C∗-algebra of a non-trivial group has unique tracial state, respectively, is simple, in terms of Dixmier-type properties of the group C∗-algebra. We also give a
Characterizations of C*-simplicity
We characterize discrete groups that are C*-simple, meaning that their reduced C*-algebra is simple. First, we prove that a discrete group is C*-simple if and only if it has Powers' averaging
Characterization of linear groups whose reduced C*-algebras are simple
The reduced C*-algebra of a countable linear group G is shown to be simple if and only if G has no nontrivial normal amenable subgroups. Moreover, these conditions are shown to be equivalent to the
Cocompact amenable closed subgroups: weakly inequivalent representations in the left-regular representation
We show that if $H \leq G$ is a closed amenable and cocompact subgroup of a unimodular locally compact group, then the reduced group C*-algebra of $G$ is not simple. Equivalently, there are unitary
...
...