Sums of commutators in pure C*-algebras

  title={Sums of commutators in pure C*-algebras},
  author={Ping Wong Ng and Leonel Robert},
  journal={arXiv: Operator Algebras},
In a pure C ∗ -algebra (i.e., one having suitable regularity proper- ties in its Cuntz semigroup), any element on which all bounded traces vanish is a sum of 7 commutators. 
Nuclear dimension of simple stably projectionless C∗-algebras
We prove that Z-stable, simple, separable, nuclear, non-unital C*-algebras have nuclear dimension at most 1. This completes the equivalence between finite nuclear dimension and Z-stability forExpand
The Model Theory of Nuclear $\mathrm{C}^*$-algebras
We begin the model theoretic study of nuclear $\mathrm{C}^*$-algebras using the tools of continuous logic.
Normal subgroups of invertibles and of unitaries in a C*-algebra
  • L. Robert
  • Mathematics
  • Journal für die reine und angewandte Mathematik (Crelles Journal)
  • 2019
Abstract We investigate the normal subgroups of the groups of invertibles and unitaries in the connected component of the identity of a C * {\mathrm{C}^{*}} -algebra. By relating normal subgroups toExpand
Simplicity, bounded normal generation, and automatic continuity of groups of unitaries
We show that the commutator subgroup of the group of unitaries connected to the identity in a simple unital C*-algebra is simple modulo its center. We then go on to investigate the role ofExpand
Purely infinite corona algebras
Let A be a simple, sigma-unital, non-unital C*-algebra, with metrizable tracial simplex T(A), which is projection-surjective and injective and has strict comparison of positive elements by traces.Expand
The Dixmier property and tracial states for C⁎-algebras
A.T. was partially supported by an NSERC Postdoctoral Fellowship and through the EPSRC grant EP/N00874X/1. Acknowledgements We are grateful to Luis Santiago for helpful discussions at an early stageExpand
Covering Dimension of C*-Algebras and 2-Coloured Classification
We introduce the concept of finitely coloured equivalence for unital *-homomorphisms between C*-algebras, for which unitary equivalence is the 1-coloured case. We use this notion to classifyExpand
Strict Comparison of Positive Elements in Multiplier Algebras
Abstract Main result: If a ${{C}^{*}}$ -algebra $\mathcal{A}$ is simple, $\sigma $ -unital, has finitely many extremal traces, and has strict comparison of positive elements by traces, then itsExpand


In a simple C*-algebra with suitable regularity properties, any unitary or invertible element with de la Harpe-Skandalis determi- nant zero is a finite product of commutators.
Finite sums of commutators
We show that elements of unital C*-algebras without tracial states are finite sums of commutators. Moreover, the number of commutators involved is bounded, depending only on the given C*-algebra.
On the linear span of the projections in certain simple C*-algebras
In this paper we show that if a C*-algebra A admits a certain 3 × 3 matrix decomposition, then every commutator in A can be written as a linear combination of at most 84 projections in A. In certainExpand
Dixmier approximation and symmetric amenability for C*-algebras
We study some general properties of tracial C*-algebras. In the first part, we consider Dixmier type approximation theorem and characterize symmetric amenability for C*-algebras. In the second part,Expand
Let $\mathcal{Z}$ be the Jiang–Su algebra and let τ be its unique tracial state. We prove that for all $a \in \mathcal{Z}$, the following statements are equivalent: (1) a is a finite sum ofExpand
The Jiang–Su algebra revisited
Abstract We give a number of new characterizations of the Jiang–Su algebra 𝒵, both intrinsic and extrinsic, in terms of C*-algebraic, dynamical, topological and K-theoretic conditions. Along the wayExpand
$\mathcal Z$-stability and finite dimensional tracial boundaries
We show that a simple separable unital nuclear nonelementary $C^*$-algebra whose tracial state space has a compact extreme boundary with finite covering dimension admits uniformly tracially largeExpand
Equivalence and traces on C∗-algebras
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
Traces, unitary characters and crossed products by Z
We determine the character group of the infinite unitary group of a unital exact C*-algebra in terms of K-theory and traces and obtain a description of the infinite unitary group modulo the closureExpand
Classification of inductive limits of 1-dimensional NCCW complexes
A classification result is obtained for the C*-algebras that are (stably isomorphic to) inductive limits of 1-dimensional noncommutative CW complexes with trivial $K_1$-group. The classifying functorExpand