Covering Dimension of C*-Algebras and 2-Coloured Classification

Released on by Joan Bosa
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  • Covering Dimension of C*-Algebras and 2-Coloured Classification Book Detail

  • Author : Joan Bosa
  • Release Date : 2019-02-21
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 112
  • ISBN 13 : 1470434709
  • File Size : 66,66 MB
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Covering Dimension of C*-Algebras and 2-Coloured Classification by Joan Bosa PDF Summary

Book Description: The authors introduce the concept of finitely coloured equivalence for unital -homomorphisms between -algebras, for which unitary equivalence is the -coloured case. They use this notion to classify -homomorphisms from separable, unital, nuclear -algebras into ultrapowers of simple, unital, nuclear, -stable -algebras with compact extremal trace space up to -coloured equivalence by their behaviour on traces; this is based on a -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, -stable -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 -algebras with finite nuclear dimension.

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