Obstructions to 𝒵-Stability for Unital Simple C *-Algebras

By G. Gong, Xinhui Jiang, Hongbing Su. Canadian mathematical bulletin, 2000

95 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bff327bba3cdbdf0d9d5670ac4ed8df63a3c2495

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In Applied Mathematics

1. W. Winter
2. Andrew S. Toms
3. M. Rørdam
4. Huaxin Lin
5. Ilan Hirshberg
6. G. Elliott
7. F. Perera
8. Z. Niu

In Mathematical Physics

1. W. Winter
2. Andrew S. Toms
3. Z. Niu
4. G. Elliott
5. Huaxin Lin
6. F. Perera
7. David Kerr
8. G. Gong

Citations in the corpus

• The stable and the real rank of Z-absorbing C*-algebras (2004, background): “(iv) If A is simple and unital, then the stable rank of A is one if and only if A is finite.”
• C_0(X)-algebras, stability and strongly self-absorbing C*-algebras (2006, background): “Algebras which absorb the Jiang–Su algebra tend to be well-behaved in many respects, and thus, Z-stability can be seen as a regularity property, which needs to be better understood (see [10, 32, 34, 35, 36, 37]).”
• Recasting the Elliott conjecture (2006, background): “Indeed, this fact is obvious if one considers only algebras with weakly unperforated ordered K0-groups (a condition which holds in every confirmation of (EC)) — by Theorem 1 of [13], the tensor product of such and algebra, say A, with Z has the same Elliott invariant as A, and so (EC) predicts that ”
• Classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras (2014, background): “The existence of non-elementary simple C∗-algebras which was not Z stable, was first proved by Gong-Jiang-Su (see [32]).”
• FLAT DIMENSION GROWTH FOR C ∗ -ALGEBRAS (2005, background): “Proof. The algebra Ac of Theorem 5.1 has a perforated ordered K0-group for each c 6= 0. Theorem 1 of [ 12 ] states that a simple, unital, finite, and Z-stable C ∗algebra has a weakly unperforated ordered K0-group, whence the Acs in question are non-Z-stable.”
• Regularity properties in the classification program for separable amenable C*-algebras (2007, unknown): “2 (Gong-Jiang-Su, [28]).”
• The classification of simple separable KK-contractible C*-algebras with finite nuclear dimension (2016, background): “Now since B is unital and B ⊗ K is Z-stable, by [21] (see also 4.”
• A classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras, I: $C^*$-algebras with generalized tracial rank one. (2018, background): “If A is a simple separable amenable C∗-algebra with weakly unperforated K0(A) which belongs to a classifiable class, then one should expect A to be isomorphic to A⊗Z, since these two algebras have the same Elliott invariant (Theorem 1 of [36]).”
• K-Theory for operator algebras. Classification of C$^*$-algebras (2009, background): “Indeed, we have the following (that can be found in [ 30 ]):”