# Simplicity and tracial weights on non-unital reduced crossed products

@inproceedings{Suzuki2021SimplicityAT, title={Simplicity and tracial weights on non-unital reduced crossed products}, author={Yuhei Suzuki}, year={2021} }

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 reduced crossed product over discrete C∗-simple groups, and a similar result for uniqueness of tracial weight. Interestingly, our analysis on tracial weights involves von Neumann algebra theory. Our generalizations have two applications. The first is to locally compact groups. We establish stability… Expand

#### References

SHOWING 1-10 OF 23 REFERENCES

Reduced twisted crossed products over C*-simple groups

- Mathematics
- 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… Expand

A New Look at C∗-Simplicity and the Unique Trace Property of a Group

- Mathematics
- 2015

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… Expand

Twisted crossed products of C *-algebras

- Mathematics
- 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… Expand

C*-simplicity and the unique trace property for discrete groups

- Mathematics
- 2014

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… Expand

Boundaries of reduced C*-algebras of discrete groups

- Mathematics
- 2014

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… Expand

On simplicity of reduced C*-algebras of groups

- Mathematics
- 2005

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… Expand

Equivalence and traces on C∗-algebras

- Mathematics
- 1979

Abstract We introduce an equivalence relation among the positive elements in a C∗ and show that the algebra is (semi-) finite if and only if there is a separating family of (semi-) finite traces.… Expand

Non-amenable tight squeezes by Kirchberg algebras

- Mathematics
- Mathematische Annalen
- 2021

We give a framework to produce C*-algebra inclusions with extreme properties. This gives the first constructive nuclear minimal ambient C*-algebras. We further obtain a purely infinite analogue of… Expand

Crossed products and the Mackey-Rieffel-Green machine

- Mathematics
- 2017

If a locally compact group G acts continuously via *-automorphisms on a C*-algebra A, one can form the full and reduced crossed products \(A \rtimes G \;\mathrm{and}\;A\rtimes_{r}G\) of A by G.

C*-simplicity of locally compact Powers groups

- Mathematics
- Journal für die reine und angewandte Mathematik (Crelles Journal)
- 2019

In this article we initiate research on locally compact
\mathrm{C}^{*}
-simple groups. We first show that every
\mathrm{C}^{*}
-simple group must be totally disconnected. Then… Expand