Abstract
It is shown that all 2-quasitraces on a unital exact C ∗
-algebra are traces. As consequences one gets: (1) Every stably finite exact unital C ∗
-algebra has a tracial state, and (2) if an AW ∗
-factor of type II 1
is generated (as an AW ∗
-algebra) by an exact C ∗
-subalgebra, then it is a von Neumann II 1
-factor. This is a partial solution to a well known problem of Kaplansky. The present result was used by Blackadar, Kumjian and Rørdam to prove that RR(A)=0
for every simple non-commutative torus of any dimension
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Comptes Rendus Mathematiques de l'Academie des Sciences = Mathematical reports of the academy of science |
| Vol/bind | 36 |
| Udgave nummer | 2-3 |
| Sider (fra-til) | 67-92 |
| ISSN | 0706-1994 |
| Status | Udgivet - 2014 |