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Perforated Ordered $\K_0$-Groups

  Published:2000-12-01
 Printed: Dec 2000
  • George A. Elliott
  • Jesper Villadsen
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Abstract

A simple $\C^*$-algebra is constructed for which the Murray-von Neumann equivalence classes of projections, with the usual addition---induced by addition of orthogonal projections---form the additive semi-group $$ \{0,2,3,\dots\}. $$ (This is a particularly simple instance of the phenomenon of perforation of the ordered $\K_0$-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.)
MSC Classifications: 46L35, 46L80 show english descriptions Classifications of $C^*$-algebras
$K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
46L35 - Classifications of $C^*$-algebras
46L80 - $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
 

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