Semilattices of groups and inductive limits of Cuntz algebras
| dc.creator | Goodearl, K. R. | |
| dc.creator | Pardo, E. | |
| dc.creator | Wehrung, F. | |
| dc.date | 2004-08-05 | |
| dc.date.accessioned | 2026-07-07T05:11:03Z | |
| dc.date.available | 2026-07-07T05:11:03Z | |
| dc.description | We characterize, in terms of elementary properties, the abelian monoids which are direct limits of finite direct sums of monoids of the form $(Z/nZ)\sqcup\{0\}$ (where 0 is a new zero element), for positive integers $n$. The key properties are the Riesz refinement property and the requirement that each element $x$ has finite order, that is, $(n+1)x=x$ for some positive integer $n$. Such monoids are necessarily semilattices of abelian groups, and part of our approach yields a characterization of the Riesz refinement property among semilattices of abelian groups. Further, we describe the monoids in question as certain submonoids of direct products $Λ\times G$ for semilattices $Λ$ and torsion abelian groups $G$. When applied to the monoids $V(A)$ appearing in the non-stable K-theory of C*-algebras, our results yield characterizations of the monoids $V(A)$ for C* inductive limits $A$ of sequences of finite direct products of matrix algebras over Cuntz algebras $O_n$. In particular, this completely solves the problem of determining the range of the invariant in the unital case of Rørdam's classification of inductive limits of the above type. | |
| dc.identifier | https://arxiv.org/abs/math/0408072 | |
| dc.identifier | http://arxiv.org/abs/math/0408072 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72116 | |
| dc.subject | Operator Algebras | |
| dc.subject | 20M17; 46L35; 06A12; 06F05 | |
| dc.title | Semilattices of groups and inductive limits of Cuntz algebras | |
| dc.type | text |