Articles liés à Covering Dimension of C*-algebras and 2-coloured Classificat...

Covering Dimension of C*-algebras and 2-coloured Classification - Couverture souple

Bosa, Joan; Brown, Nathanial P.; Sato, Yasuhiko; Tikuisis, Aaron; White, Stuart

 
9781470434700: Covering Dimension of C*-algebras and 2-coloured Classification
Couverture souple
ISBN 10 : 1470434709 ISBN 13 : 9781470434700
Editeur : American Mathematical Society, 2019

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l'auteur

Joan Bosa, University of Glasgow, Scotland, United Kingdom.

Nathanial P. Brown, The Pennsylvania State University, University Park, Pennsylvania.

Yasuhiko Sato, Kyoto University, Japan.

Aaron Tikuisis, University of Aberdeen, Scotland, United Kingdom.

Stuart White, University of Glasgow, Scotland, United Kingdom, and University of Munster, Germany.

Wilhelm Winter, University of Munster, Germany.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2019
Langue
anglais
ISBN 10 
1470434709
ISBN 13 
9781470434700
Reliure
Broché
Nombre de pages
97
Coordonnées du fabricant
Buchpark GmbH
https://www.buchpark.de

Krügerweg 1
Trebbin
Brandenburg
14959
Allemagne