Decomposition rank of UHF-absorbing C*-algebras
Operator Algebras
2015-01-14 v2
Abstract
Let A be a unital separable simple C*-algebra with a unique tracial state. We prove that if A is nuclear and quasidiagonal, then A tensored with the universal UHF-algebra has decomposition rank at most one. Then it is proved that A is nuclear, quasidiagonal and has strict comparison if and only if A has finite decomposition rank. For such A, we also give a direct proof that A tensored with a UHF-algebra has tracial rank zero. Applying this characterization, we obtain a counter-example to the Powers-Sakai conjecture.
Keywords
Cite
@article{arxiv.1303.4371,
title = {Decomposition rank of UHF-absorbing C*-algebras},
author = {Hiroki Matui and Yasuhiko Sato},
journal= {arXiv preprint arXiv:1303.4371},
year = {2015}
}
Comments
19 pages, a counter example to the Powers-Sakai conjecture added