Strongly self-absorbing C*-algebras are Z-stable

By W. Winter. 2009

88 citations recorded by the source corpus.

We prove the title. This characterizes the Jiang-Su algebra Z as the uniquely determined initial object in the category of strongly self-absorbing C*-algebras.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bbc12df9c257a471ea2905e0926b9f396fb80f91

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Nuclear dimension and $$\mathcal Z$$Z-stability (2014, background): “In [48], Z was characterised in an entirely abstract manner as the initial object in the category of strongly self-absorbing C∗-algebras.”
Equivariant Kirchberg–Phillips-Type Absorption for Amenable Group Actions (2016, background): “Indeed, for the Jiang–Su algebra Z , which is the initial object in the category of strongly self-absorbing C∗-algebras [81], the most general analogue of the McDuff property is given by Z-stability and plays a major role in the Elliott program through the Toms–Winter regularity conjecture [15,82,83”
Nuclear dimension and -stability of pure C ∗ -algebras (2010, background): “In [29], several alternative characterizations of the Jiang–Su algebra were given; see also [10, 41].”
Strongly self-absorbing *-dynamical systems (2015, background): “We note that the K1-injectivity criterion in both [25] and [49] has turned out to be redundant due to the main result of [51].”
Quasidiagonality of nuclear C*-algebras (2015, background): “These are simple, nuclear, with at most one trace (results that go back to [27]) and are Z-stable by [79].”
Nuclear dimension of simple $$\mathrm {C}^*$$-algebras (2019, background): “It satisfies Z ⊗ Z ∼= Z; moreover, this isomorphism occurs in a particularly strong way, analogous to the corresponding statement for R (see [66]), and Z is the minimal non-trivial C-algebra with this property ([73]).”
Strict comparison and $$ \mathcal{Z} $$-absorption of nuclear C∗-algebras (2011, background): “Winter also showed that Z is the initial object in the category of strongly self-absorbing C∗-algebras [25].”
A Dixmier-Douady Theory for strongly self-absorbing C*-algebras II: the Brauer group (2014, background): “Under the assumptions of the lemma, it is known that K0(D) is torsion free (by [17]) and that D has cancellation of full projections by [19] and [15].”
Covering Dimension of C*-Algebras and 2-Coloured Classification (2015, background): “Indeed, the Jiang-Su algebra Z is the minimal nontrivial unital C∗-algebra D which has two fundamental properties enjoyed by R: D ∼= D ⊗ D and every unital endomorphism of D is approximately inner [69].”
The Rohlin property for automorphisms of the Jiang-Su algebra (2009, unknown): “Keywords: C∗-algebra, automorphism, Jiang-Su algebra, Rohlin prop- erty.”