Covering Dimension of C*-Algebras and 2-Coloured Classification
Joan Bosa, Nathanial P. Brown, Yasuhiko Sato
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.
년:
2018
판:
1
출판사:
American Mathematical Society
언어:
english
페이지:
112
ISBN 10:
1470449498
ISBN 13:
9781470449490
시리즈:
Memoirs of the American Mathematical Society Ser.
파일:
PDF, 1.12 MB
IPFS:
,
english, 2018