A New Look at C∗-Simplicity and the Unique Trace Property of a Group
By Uffe Haagerup. 2015
53 citations recorded by the source corpus.
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 simple proof of the recent result by Breuillard, Kalantar, Kennedy and Ozawa that the reduced C∗-algebra of a group has unique tracial state if and only if the amenable radical of the group is trivial.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/be2aebe4522dd14cb9307898cd7a0e5de5db7fe6
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- M. Kennedy
- Mehrdad Kalantar
- Emmanuel Breuillard
- Nathanial P. Brown Narutaka Ozawa
- E. Guentner
- Sorin Popa
- S. Vaes
- Adrian Ioana
In Mathematical Physics
- M. Kennedy
- Mehrdad Kalantar
- Emmanuel Breuillard
- Nathanial P. Brown Narutaka Ozawa
- Gilles Pisier
- Adrian Ioana
- Sorin Popa
- E. Guentner
Citations in the corpus
- An intrinsic characterization of C*-simplicity (2015, unknown): “Thus we obtain another proof of Haagerup and Olesen’s result [12] that if T is C*-simple, then F is non-amenable.”
- C*-simplicity and the unique trace property for discrete groups (2014, methodology): “Subsequently, Kennedy [34] and Haagerup in a posthumous preprint [27] independently discovered a new characterization of C*-simplicity.”