Nuclear dimension of simple $$\mathrm {C}^*$$-algebras

By Jorge Castillejos, Samuel Evington, Aaron Tikuisis, Stuart White, W. Winter. Inventiones Mathematicae, 2019

83 citations recorded by the source corpus.

<jats:p>We compute the nuclear dimension of separable, simple, unital, nuclear, <jats:inline-formula><jats:alternatives><jats:tex-math>$${\mathcal {Z}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Z</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>-stable <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathrm {C}^*$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula>-algebras. This makes classification accessible from <jats:inline-formula><jats:alternatives><jats:tex-math>$${\mathcal {Z}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Z</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>-stability and in particular brings large classes of <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathrm {C}^*$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula>-algebras associated to free and minimal actions of amenable groups on finite dimensional spaces within the scope of the Elliott classification programme.</jats:p>

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3e02012907cddb3449cb3aec2bb19864af2ceabd

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In Algebra and Number Theory

1. Samuel Evington
2. Jorge Castillejos
3. David Kerr
4. G'abor Szab'o
5. Frederic Pierre Jean Latrémolière
6. A. Kavruk

In Applied Mathematics

1. Samuel Evington
2. Jorge Castillejos
3. David Kerr
4. G'abor Szab'o

In Mathematical Physics

1. David Kerr
2. Samuel Evington
3. Jorge Castillejos
4. G'abor Szab'o
5. Hanfeng Li
6. Ben Hayes
7. Xiangdong Ye
8. Eli Glasner

Citations in the corpus

• Nuclear dimension of simple stably projectionless C∗-algebras (2019, methodology): “ebraically simple. There can be non-trivial (nonclosed) ideals. Examples of such ideals are the domains of unbounded traces, which may now exist and must therefore be taken into account. Furthermore, [15] builds on the foundations of [8], which has a global assumption of unitality and makes explicit”
• Almost Finiteness and the Small Boundary Property (2018, background): “d 1−ϕ(1) is small in the sense of Cuntz subequivalence [19].2 The most recent affirmation of this analogy is the work of Castillejos, Evington, Tikuisis, White, and Winter on the Toms–Winter conjecture [4], which shows that Z-stability can be substituted for finite nuclear dimension as the regularity h”