Covering Dimension of C*-Algebras and 2-Coloured Classification (Paperback)

The authors introduce the concept of finitely coloured equivalence for unital $^*$-homomorphisms between $\mathrm C^*$-algebras, for which unitary equivalence is the $1$-coloured case. They use this notion to classify $^*$-homomorphisms from separable, unital, nuclear $\mathrm C^*$-algebras into ultrapowers of simple, unital, nuclear, $\mathcal Z$-stable $\mathrm C^*$-algebras with compact extremal trace space up to $2$-coloured equivalence by their behaviour on traces; this is based on a $1$-coloured classification theorem for certain order zero maps, also in terms of tracial data. As an application the authors calculate the nuclear dimension of non-AF, simple, separable, unital, nuclear, $\mathcal Z$-stable $\mathrm C^*$-algebras with compact extremal trace space: it is 1. In the case that the extremal trace space also has finite topological covering dimension, this confirms the remaining open implication of the Toms-Winter conjecture. Inspired by homotopy-rigidity theorems in geometry and topology, the authors derive a ``homotopy equivalence implies isomorphism'' result for large classes of $\mathrm C^*$-algebras with finite nuclear dimension.

General

Imprint:	American Mathematical Society
Country of origin:	United States
Series:	Memoirs of the American Mathematical Society
Release date:	December 2018
Authors:	Joan Bosa • Nathanial P. Brown • Yasuhiko Sato • Aaron Tikuisis • Stuart White
Dimensions:	254 x 178mm (L x W)
Format:	Paperback
Pages:	97
ISBN-13:	978-1-4704-3470-0
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > General
LSN:	1-4704-3470-9
Barcode:	9781470434700

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