Riesz properties of K-groups associated to C*-algebras of minimal ranks.
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 K_{0}(A) being weakly
unperforated.
- Remarks:
- Access opportunities:
Not available electronically as publishing rights have been transfered.
eilers@math.ku.dk/July
2004.