RT journal article
T1 Semilattices of groups and inductive limits of Cuntz algebras
A1 Goodearl, K.R.
A1 Pardo Espino, Enrique
A1 Wehrung, F.
A2 Matemáticas
AB We characterize, in terms of elementary properties, the abelian monoidswhich are direct limits of finite direct sums of monoids of the form ðZ=nZÞ t f0g (where 0 isa new zero element), for positive integers n. The key properties are the Riesz refinementproperty and the requirement that each element x has finite order, that is, ðn þ 1Þx ¼ x forsome positive integer n. Such monoids are necessarily semilattices of abelian groups, andpart of our approach yields a characterization of the Riesz refinement property amongsemilattices of abelian groups. Further, we describe the monoids in question as certainsubmonoids of direct products L   G for semilattices L and torsion abelian groups G.When applied to the monoids VðAÞ appearing in the non-stable K-theory of C*-algebras,our results yield characterizations of the monoids VðAÞ for C* inductive limits A of sequencesof finite direct products of matrix algebras over Cuntz algebras On. In particular,this completely solves the problem of determining the range of the invariant in the unitalcase of Rørdam’s classification of inductive limits of the above type.
PB De Gruyter
SN 1435-5345
YR 2005
FD 2005-01-01T00:00:00Z
LK http://hdl.handle.net/10498/16078
UL http://hdl.handle.net/10498/16078
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026