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Andrew Toms - Perforated K0-groups of $C^\ast-$algebras

ANDREW TOMS, Fields Institute, University of Toronto, Toronto, Ontario, Canada
Perforated K0-groups of $C^\ast-$algebras

Every weakly unperforated ordered abelian group arises as the K0-group of some simple, separable $C^\ast-$algebra. What of perforated abelian groups? In this talk we outline methods for constructing $C^\ast-$algebras having a maximal free cyclic subgroup of K0, say H, with the property that $H \cap K_0^+ \simeq \langle
\rangle$, k and l relatively prime positive integers. The methods used also provide many other such algebras with subgroups whose intersection with the positive cone of K0 further extend the preceding result, though these are less succinctly described.