Cancellation does not imply stable rank one
Operator Algebras
2007-05-23 v2 Mathematical Physics
math.MP
Abstract
An 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, and some partial convereses have been established. We prove that cancellation does not imply stable rank one for simple, stably finite C*-algebras.
Keywords
Cite
@article{arxiv.math/0509107,
title = {Cancellation does not imply stable rank one},
author = {Andrew S. Toms},
journal= {arXiv preprint arXiv:math/0509107},
year = {2007}
}
Comments
4 pages, exposition improved in proof of main theorem, to appear in Bull. LMS