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Bulletin of the London Mathematical Society Advance Access originally published online on June 12, 2009
Bulletin of the London Mathematical Society 2009 41(4):639-653; doi:10.1112/blms/bdp037
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© 2009 London Mathematical Society

A direct proof of Z-stability for approximately homogeneous C*-algebras of bounded topological dimension

Marius Dadarlat

Department of Mathematics
Purdue University
150 N. University Street
West Lafayette, IN 47907-2067
USA
mdd@math.purdue.edu

N. Christopher Phillips

Department of Mathematics
University of Oregon
Eugene, OR 97403-1222
USA
ncp@darkwing.uoregon.edu

Andrew S. Toms

Department of Mathematics and Statistics
York University
4700 Keele Street
Toronto
Ontario
Canada M3J 1P3

Received 5 September 2008. Revision received 4 February 2009.

We prove that a unital simple approximately homogeneous C*-algebra with no dimension growth absorbs the Jiang–Su algebra tensorially without appealing to the classification theory of these algebras. Our main result continues to hold under the slightly weaker hypothesis of exponentially slow dimension growth.

2000 Mathematics Subject Classification 46L35 (primary), 46L80 (secondary).

Marius Dadarlat was partially supported by NSF grant DMS-0500693. N. Christopher Phillips was partially supported by NSF grant DMS-0701076, by the Fields Institute for Research in Mathematical Sciences, Toronto, Canada, and by an Elliott Distinguished Visitorship at the Fields Institute. Andrew S. Toms was partially supported by NSERC.


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