Strong perforation in infinitely generated K_0-groups of simple C*-algebras

Details Strong perforation in infinitely generated K_0-groups of simple C*-algebras Strong perforation in infinitely generated K_0-groups of simple C*-algebras

2005-09-19

arxiv.org/abs/math/0509425v1

Math. Scand. 96 (2005), pp. 147-160

Mathematics

Operator Algebras

15 pages

Scientific paper

Let (G,G^+) be a simple ordered abelian group. We say that G has strong perforation if there exists a non-positive element x in G such that nx is positive and non-zero for some natural number n. Otherwise, the group is said to be weakly unperforated. Examples of simple C*-algebras whose ordered K_0-groups have this property and for which the entire order structure on K_0 is known have, until now, been restricted to the case where K_0 is group isomorphic to the integers. We construct simple, separable, unital C*-algebras with strongly perforated K_0-groups group isomorphic to an arbitrary infinitely generated subgroup of the rationals, and determine the order structure on K_0 in each case.

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