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Titel: Covering Dimension of C*-Algebras and 2-Coloured Classification Zustand: New Autor: Yasuhiko Sato, Joan Bosa, Aaron Tikuisis, Nathanial P. Brown, Stuart White Produktart: Taschenbuch EAN: 9781470434700 ISBN: 9781470434700 Verlag: American Mathematical Society Genre: Science Nature & Math Release date: 30/03/2019 Description: 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. Sprache: Englisch Herstellungsland und -region: US Höhe: 254mm Länge: 178mm Gewicht: 210g Buchreihe: Memoirs of the American Mathematical Society Information fehlt?
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