Simple real rank zero algebras with locally Hausdorff spectrum

Author:
Ping Wong Ng

Journal:
Proc. Amer. Math. Soc. **134** (2006), 2223-2228

MSC (2000):
Primary 46L35

DOI:
https://doi.org/10.1090/S0002-9939-06-07916-0

Published electronically:
March 14, 2006

MathSciNet review:
2213694

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a unital, simple, separable -algebra with real rank zero, stable rank one, and weakly unperforated ordered group. Suppose, also, that can be locally approximated by type I algebras with Hausdorff spectrum and bounded irreducible representations (the bound being dependent on the local approximating algebra). Then is tracially approximately finite dimensional (i.e., has tracial rank zero).

Hence, is an -algebra with bounded dimension growth and is determined by -theoretic invariants.

The above result also gives the first proof for the locally case.

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Additional Information

**Ping Wong Ng**

Affiliation:
Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3

Address at time of publication:
The Fields Institute for Research in Mathematical Sciences, 222 College Street, Toronto, Ontario, Canada M5T 3J1

Email:
pwn@erdos.math.unb.ca

DOI:
https://doi.org/10.1090/S0002-9939-06-07916-0

Received by editor(s):
November 21, 2003

Received by editor(s) in revised form:
June 23, 2004

Published electronically:
March 14, 2006

Communicated by:
David R. Larson

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.