Quasitraces on exact C*-algebras are traces
Research output: Contribution to journal › Journal article › Research › peer-review
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
Original language | English |
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Journal | Comptes Rendus Mathematiques de l'Academie des Sciences = Mathematical reports of the academy of science |
Volume | 36 |
Issue number | 2-3 |
Pages (from-to) | 67-92 |
ISSN | 0706-1994 |
Publication status | Published - 2014 |
ID: 137628477