Nuclear dimension of simple $$\mathrm {C}^*$$-algebras-Reference-Cited by-同舟云学术

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

Published:2020-12-22 Issue:1 Volume:224 Page:245-290
ISSN:0020-9910
Container-title:Inventiones mathematicae
language:en
Short-container-title:Invent. math.

Author:

Castillejos Jorge,Evington Samuel,Tikuisis Aaron,White Stuart,Winter Wilhelm

Abstract

AbstractWe compute the nuclear dimension of separable, simple, unital, nuclear,

$${\mathcal {Z}}$$

Z -stable

$$\mathrm {C}^*$$

C ∗ -algebras. This makes classification accessible from

$${\mathcal {Z}}$$

Z -stability and in particular brings large classes of

$$\mathrm {C}^*$$

C ∗ -algebras associated to free and minimal actions of amenable groups on finite dimensional spaces within the scope of the Elliott classification programme.

Funder

Westfälische Wilhelms-Universität Münster

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

http://link.springer.com/content/pdf/10.1007/s00222-020-01013-1.pdf

Reference79 articles.

1. Blackadar, B.: Operator algebras, volume 122 of Encyclopaedia of Mathematical Sciences. Springer-Verlag, Berlin. Theory of $${{\rm C}}^{*}$$-algebras and von Neumann algebras. Operator Algebras and Non-commutative Geometry, III (2006)

2. Blackadar, B., Kirchberg, E.: Generalized inductive limits of finite-dimensional $${{\rm C}}^*$$-algebras. Math. Ann. 307(3), 343–380 (1997)

3. Bosa, J., Brown, N., Sato, Y., Tikuisis, A., White, S., Winter, W.: Covering dimension of $${{\rm C}}^*$$-algebras and 2-coloured classification. Mem. Am. Math. Soc. 257(1233), viii+97 (2019)

4. Brown, N.: Invariant means and finite representation theory of $${{\rm C}}^*$$-algebras. Mem. Am. Math. Soc. 184(865), viii+105 (2006)

5. Brown, N., Carrión, J., White, S.: Decomposable approximations revisited. In: Operator Algebras and Applications: The Abel Symposium 2015, volume 12 of Abel Symp., pp. 45–65. Springer (2016)

Cited by 65 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Bauer simplices and the small boundary property;Journal of Functional Analysis;2024-12

2. A geometric Elliott invariant and noncommutative rigidity of mapping tori;Journal of Functional Analysis;2024-12

3. Remarks on Villadsen algebras;Journal of Functional Analysis;2024-10

4. Nuclear dimension of graph *-algebras with Condition (K);Proceedings of the American Mathematical Society;2024-08-23

5. On classification of nonunital amenable simple C*-algebras, IV: Stably projectionless C*-algebras;Annals of K-Theory;2024-08-18