Cancellation does not imply stable rank one

Details Cancellation does not imply stable rank one Cancellation does not imply stable rank one

2005-09-05

arxiv.org/abs/math/0509107v2

Mathematics

Operator Algebras

4 pages, exposition improved in proof of main theorem, to appear in Bull. LMS

Scientific paper

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.

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