Journal article
Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence
Journal für die reine und angewandte Mathematik, Vol.640(640), pp.135-165
03/2010
DOI: 10.1515/crelle.2010.023
Abstract
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 we construct a directed graph E such that 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.
Details
- Title: Subtitle
- Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence
- Creators
- Takeshi Katsura - Department of Mathematics, Keio University, Yokohama, 223-8522, Japan. e-mail: katsura@math.keio.ac.jpPaul S Muhly - Department of Mathematics, University of Iowa, Iowa City, IA 52242-1419, USA. e-mail: pmuhly@math.uiowa.eduAidan Sims - School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia. e-mail: asims@uow.edu.auMark Tomforde - Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA. e-mail: tomforde@math.uh.edu
- Resource Type
- Journal article
- Publication Details
- Journal für die reine und angewandte Mathematik, Vol.640(640), pp.135-165
- Publisher
- Walter de Gruyter GmbH & Co. KG
- DOI
- 10.1515/crelle.2010.023
- ISSN
- 0075-4102
- eISSN
- 1435-5345
- Language
- English
- Date published
- 03/2010
- Academic Unit
- Mathematics; Statistics and Actuarial Science
- Record Identifier
- 9984083207502771
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