Infinite Non-simple C*-Algebras: Absorbing the Cuntz Algebra O∞

By Eberhard Kirchberg, M. Rørdam. 2002

194 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5f1ebdb15cf96a3a4ad5e3d200c42c14b321e60c

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

1. W. Winter
2. Andrew S. Toms
3. M. Rørdam
4. G. Elliott
5. Ilan Hirshberg
6. F. Perera
7. Leonel Robert
8. G'abor Szab'o

In Mathematical Physics

1. W. Winter
2. Andrew S. Toms
3. M. Rørdam
4. Leonel Robert
5. G. Elliott
6. F. Perera
7. G'abor Szab'o
8. Ilan Hirshberg

In Statistical and Nonlinear Physics

1. W. Winter
2. Andrew S. Toms
3. Ilan Hirshberg
4. G. Elliott
5. M. Rørdam
6. Eberhard Kirchberg
7. F. Perera
8. P. Ara

Citations in the corpus

• K-Theory for operator algebras. Classification of C$^*$-algebras (2009, background): “The theorem below (proved in [ 41 ]) follows this spirit.”
• The Cuntz semigroup as an invariant for C*-algebras (2007, methodology): “M. Rørdam, Classification of nuclear, simple C*-algebras, pages 1–145 of Clas- sification of nuclear C*-algebras.”
• Purely infinite C*-algebras of real rank zero (2006, methodology): “14 below was shown in [13] by Kirchberg and the second named author for C -algebras of the real rank zero.”
• Large subalgebras (2014, unknown): “2 of [18], there is d ∈ K ⊗ A such that dcd = (a − ε)+.”
• COVERING DIMENSION AND QUASIDIAGONALITY (2002, background): “This example is purely infinite in the sense of [10] and has decomposition rank one.”
• Purely infinite C*-algebras arising from crossed products (2010, background): “† A C∗-algebra is in [18] said to be traceless if it admits no non-zero lower semi-continuous (possibly unbounded) 2-quasitraces defined on an algebraic ideal of the given C∗-algebra.”
• The primitive ideal space of the $C^{*}$-algebras of infinite graphs (2002, background): “In fact, we think that graph algebras might play a prominent role in the study and classification of this interesting class of C ∗-algebras, whose investigations have been recently initiated by Kirchberg and Rordam [18, 19 ].”
• Rokhlin actions and self-absorbing C*-algebras (2005, background): “Absorption of O1 and O2 plays a central role in the classification theorems of Kirchberg and Phillips ([KrP, Kr1, P]), and is the focus of further study (see for instance [ KrR ]).”
• Central Sequences in C*-Algebras and Strongly Purely Infinite Algebras (2006, background): “[6], [25].”