On the classification of simple inductive limit C*-algebras, II: The isomorphism theorem

By G. Elliott, G. Gong, Liangqing Li. 2007

164 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2159e94f375806f24868cd00e498f06d9ccf01cc

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. Z. Niu
4. Huaxin Lin
5. G. Gong
6. F. Perera
7. N. Christopher Phillips
8. G. Elliott

In Mathematical Physics

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

Citations in the corpus

• Strongly self-absorbing C*-algebras (2005, background): “MR2014489 [13] Gong, G., Jiang, X. and Su, H.: Obstructions to Z-stability for unital simple C∗-algebras, Canad.”
• Classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras (2014, background): “Elliott-Gong ([23]) and Elliott-Gong-Li ([24]) (together with a reduction theorem by Gong ([31]) classified the unital simple AH-algebras with no dimension growth by the Elliott invariant (see 2.4 below).”
• Asymptotically Unitary Equivalence and Classification of Simple Amenable C*-algebras (2008, background): “4 of [11], ∆A gives an isometric isomorphism (The isomorphism follows [45] and the isometric part follows (a slight modification) proof of 3.”
• On the classification problem for nuclear C^*-algebras (2005, methodology): “simple, unital inductive limits of homogeneous algebras with contractible spectra, a class of algebras which forms the weakest and most natural extension of the very slow dimension growth AH algebras classified in [ EGL ]; both A and A ⊗U are stably finite, weakly divisible, and have property (SP), ”
• Comparison Theory and Smooth Minimal C*-Dynamics (2008, methodology): “This last result is proved using approximately homogenenous (AH) algebras of unbounded dimension growth, and so may be viewed as a strong converse to the Elliott-Gong-Li classification of simple AH algebras with no dimension growth ([ 10 ]).”
• STRUCTURE OF NUCLEAR C*-ALGEBRAS: FROM QUASIDIAGONALITY TO CLASSIFICATION AND BACK AGAIN (2017, background): “GuihuaGong, Huaxin Lin, and ZhuangNiu (2015).”
• Regularity properties in the classification program for separable amenable C*-algebras (2007, unknown): “4 (Elliott-Gong-Li and Gong, [23] and [26]).”
• Lifting KK-elements, asymptotic unitary equivalence and classification of simple C∗-algebras (2008, background): “It has been shown (see [12] and [17], also [2] and [3]) that, if in addition, A and B have tracial rank one or zero, then A and B are isomorphic if their Elliott invariant are isomorphic.”
• Nuclear dimension and -stability of pure C ∗ -algebras (2010, background): “(It should be noted, however, that the result of [11] is still a necessary step.”
• The Cuntz semigroup as an invariant for C*-algebras (2007, unknown): “(Hence by [8], if also K1(A) ∼= K1(B) then A ∼= B.”
• A classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras, I: $C^*$-algebras with generalized tracial rank one. (2018, background): “Elliott and Gong ([24]) and Elliott, Gong, Li ([25]) (together with a deep reduction theorem by Gong ([35])) classified simple AH-algebras with no dimension growth by means of the Elliott invariant (see Definition 2.”