Non-simple purely infinite C∗-algebras: the Hausdorff case

By É. Blanchard, Eberhard Kirchberg. 2004

112 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/825724215b589a3965b6c376fdfaca1018f29eed

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

Nuclear dimension of simple stably projectionless C∗-algebras (2019, background): “Since A is exact, the non-unital version of Haagerup’s Theorem gives Q (cid:101) T ( A ) = (cid:101) T ( A ) (cid:54) = 0; see [32] and [7, Remark 2.29(i)].”
Purely infinite C*-algebras of real rank zero (2006, background): “If D is a simple nuclear C -algebra, then the mapping I 7! I nD defines a lattice isomorphism from IdealðAÞ onto IdealðAnDÞ (surjectivity follows from a theorem of Blackadar, [1], see also [3], Proposition 2.”
$${\mathcal{C}}_{0}$$ (X)-algebras, stability and strongly self-absorbing $${\mathcal{C}}^{*}$$ -algebras (2007, result): “This generalizes earlier results of Blanchard and Kirchberg [ 6 ], who prove a similar statement under the additional requirements that D = O∞, X = Prim(A), and A is nuclear and stable (with different methods; see also [5] for related results).”
Nuclear dimension and Z-stability of non-simple C*-algebras (2013, result): “In the case that every simple quotient is infinite, an implication similar to (but stronger than) (ii’) ⇒ (i’) has been considered by Blanchard, Kirchberg, and Rørdam in [5, 16].”
Central Sequences in C*-Algebras and Strongly Purely Infinite Algebras (2006, background): “By [3] (and [2]) A is purely infinite if and only if A is weakly purely infinite and has”
Continuous fields of C*-algebras over finite dimensional spaces (2006, methodology): “We shall rely heavily on the classification theorem (and related results) of Kirchberg [19] and Phillips [28], and on the work on non-simple nuclear purely infinite C*-algebras of Blanchard and Kirchberg [5], [4] and Kirchberg and Rørdam [21], [22].”