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

Joan Bosa (Autor)

eBook Download: PDF

97 Seiten
American Mathematical Society (Verlag)
978-1-4704-4949-0 (ISBN)

Infos

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 "e;homotopy equivalence implies isomorphism"e; result for large classes of $/mathrm C^*$-algebras with finite nuclear dimension.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• ISBN-10: 1-4704-4949-8 / 1470449498
• ISBN-13: 978-1-4704-4949-0 / 9781470449490