Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We prove that the classes of graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence. This result answers the long-standing open question of whether every Exel-Laca algebra is Morita equivalent to a graph algebra. Given an ultragraph G we construct a directed graph E such that C*(G) is isomorphic to a full corner of C*(E). As applications, we characterize real rank zero for ultragraph algebras and describe quotients of ultragraph algebras by gauge-invariant ideals.
29 pages, 1 figure; Version 2 Comments: Minor changes and a few small typos corrected

Keywords

Operator Algebras, 46L55

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/209797

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0809.0164
 http://arxiv.org/abs/0809.0164

Collections

arXiv