Cancellation does not imply stable rank one

Andrew S. Toms

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arXiv · math/0509107

Cancellation does not imply stable rank one

Andrew S. Toms

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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.

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Andrew S. Toms. 2006-01-27. Cancellation does not imply stable rank one. https://arxiv.org/abs/math/0509107

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