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CANCELLATION DOES NOT IMPLY STABLE RANK ONE

Published online by Cambridge University Press:  19 December 2006

ANDREW S. TOMS
ANDREW S. TOMS
Affiliation:
Department of Mathematics and Statistics, York University, 4700 Keele St, Toronto, Ontario M3J 1P3, [email protected]
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Abstract

A unital C*-algebra $A$ is said to have cancellation of projections if the semigroup $D(A)$ of Murray–von Neumann equivalence classes of projections in matrices over $A$ is cancellative. It has long been known that stable rank one implies cancellation for any $A$, and some partial converses have been established. In this paper it is proved that cancellation does not imply stable rank one for simple, stably finite C*-algebras.

Keywords

46L80 (primary)46L85 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 6 , December 2006 , pp. 1005 - 1008
Copyright
The London Mathematical Society 2006

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Footnotes

This work was supported by an NSERC Postdoctoral Fellowship.