Riesz properties of K-groups associated to C*-algebras of minimal ranks

• Authors: Søren Eilers and George A. Elliott.
• Date: Final version January 2003
• Status: Comptes Rendus Mathématiques de l'Académie des Sciences (La Société Royale du Canada) 25 (2003), 108-13.
• Pages: 6
• Abstract: The equivalent interpolation and decomposition properties of Riesz and Birkhoff for ordered abelian groups play an important role in the classification theory of C*-algebras. In particular these notions have been pivotal in describing exactly which collection of K-groups are attained when the C*-algebras range in the classifiable classes.
  It was asserted in a paper by the second named author that the ordered group K_*(A) defined there has the Riesz decomposition and interpolation properties if only A has minimal stable and real ranks. Unfortunately, as was discovered when trying to generalize this statement to the case of K-groups with torsion coefficients, the proof given there is insufficient. An alternative approach can easily be amended to prove that the K_* -groups of all C*-algebras given as approximately homogeneous algebras, and with minimal ranks, have Riesz interpolation.
  It is the purpose of the present note to demonstrate how to fill the gap in the a priori much more general case of K₀(A) being weakly unperforated.
• Remarks:
• Access opportunities: Not available electronically as publishing rights have been transfered.