Perforated Ordered K0-Groups

Elliott, George A. ; Villadsen, Jesper

Canadian journal of mathematics, Tome 52 (2000) no. 6, pp. 1164-1191

Résumé

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 semigroup $$\left\{ 0,\,2,\,3,\ldots\right\}.$$ (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.)

Détail

DOI : 10.4153/CJM-2000-049-9

Mots-clés : 46L35, 46L80

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