Classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras

By G. Gong, Huaxin Lin, Z. Niu. 2014

110 citations recorded by the source corpus.

We present a classification theorem for a class of unital simple separable amenable ${\cal Z}$-stable $C^*$-algebras by the Elliott invariant. This class of simple $C^*$-algebras exhausts all possible Elliott invariant for unital stably finite simple separable amenable ${\cal Z}$-stable $C^*$-algebras. Moreover, it contains all unital simple separable amenable $C^*$-alegbras which satisfy the UCT and have finite rational tracial rank.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c255834b6e7d845365679cea866dd161b38490aa

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. Stuart White
3. Hannes Thiel
4. Aaron Tikuisis
5. G. Elliott
6. Z. Niu
7. Yasuhiko Sato
8. F. Perera

In Mathematical Physics

1. W. Winter
2. Hannes Thiel
3. Stuart White
4. Aaron Tikuisis
5. Yasuhiko Sato
6. F. Perera
7. Z. Niu
8. G. Elliott

Citations in the corpus

• Tensor products and regularity properties of Cuntz semigroups (2014, methodology): “For the said algebras that furthermore fall in the UCT class and have finite nuclear dimension, classification is now complete by the work of many authors (see [GLN15], [EGLN15], [TWW15] and the references therein).”
• On the classification of simple amenable C*-algebras with finite decomposition rank (2015, background): “This theorem can also be regarded as an abstract version (still in a special case) of the classification result of [10] and [7], where any simple unital locally approximately subhomogeneous C*-algebra is shown to be rationally tracially approximated by Elliott-Thomsen algebras (1dimensional noncommu”
• Covering Dimension of C*-Algebras and 2-Coloured Classification (2015, background): “2], as well as TAI algebras and even TA(1NCCW ) algebras (simple algebras of this form have recently been classified, under UCT- and nuclearity-hypotheses [22]).”