HAL : hal-00013765, version 2

arXiv : math.OA/0511272

DOI : 10.1007/s10977-006-0005-4

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K-Theory 37 (2006) 1--23

Versions disponibles :

v1 (10-11-2005)

v2 (27-01-2006)

Semilattices of groups and nonstable K-theory of extended Cuntz limits

Enrique Pardo 1, Friedrich Wehrung 2

(2006)

We give an elementary characterization of those (abelian) semigroups $M$ that are direct limits of countable sequences of finite direct products of monoids of the form $C\cup\{0\}$ for monogenic groups $C$. This characterization involves the Riesz refinement property together with lattice-theoretical properties of the collection of subgroups of $M$, and it makes it possible to express $M$ as a certain submonoid of a direct product $S\times G$, where $S$ is a distributive semilattice with zero and $G$ is an abelian group. When applied to the monoids $V(A)$ appearing in the nonstable K-theory of C*-algebras, our results yield a full description of $V(A)$ for C*-inductive limits $A$ of finite products of full matrix algebras over either Cuntz algebras $O_n$, where $2\leq n<\infty$, or corners of $O_{\infty}$ by projections, thus extending to the case including $O_{\infty}$ earlier work by the authors together with K.R. Goodearl.

1 :	Departamento de Matemàticas
	Universidad de Cádiz
2 :	Laboratoire de Mathématiques Nicolas Oresme (LMNO)
	CNRS : UMR6139 – Université de Caen

Domaine

:

Mathématiques/Mathématiques générales Mathématiques/Algèbres d'opérateurs

Mots Clés : Cuntz algebra – extended Cuntz limit – direct limit – inductive limit – nonstable K-theory – regular monoid – Riesz refinement – semilattice – abelian group – pure subgroup – lattice – modular – distributive

hal-00013765, version 2

http://hal.archives-ouvertes.fr/hal-00013765

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Contributeur : Friedrich Wehrung <>

Soumis le : Vendredi 27 Janvier 2006, 10:54:02

Dernière modification le : Mercredi 22 Novembre 2006, 11:32:01