Perforated Ordered K0-Groups

Abstract

AbstractA simple C*-algebra is constructed for which theMurray-von Neumann equivalence classes of projections, with the usual addition—induced by addition of orthogonal projections—form the additive semigroup{0, 2, 3, . . .}.(This is a particularly simple instance of the phenomenon of perforation of the ordered K0-group, which has long been known in the commutative case—for instance, in the case of the four-sphere—and was recently observed by the second author in the case of a simple C*-algebra.)