Journal article
TOPOLOGICAL QUIVERS
International journal of mathematics, Vol.16(7), pp.693-755
08/2005
DOI: 10.1142/S0129167X05003077
Abstract
Topological quivers are generalizations of directed graphs in which the sets of vertices and edges are locally compact Hausdorff spaces. Associated to such a topological quiver
$\mathcal{Q}$
is a C*-correspondence, and from this correspondence one may construct a Cuntz–Pimsner algebra
$C^*(\mathcal{Q})$
. In this paper we develop the general theory of topological quiver C*-algebras and show how certain C*-algebras found in the literature may be viewed from this general perspective. In particular, we show that C*-algebras of topological quivers generalize the well-studied class of graph C*-algebras and in analogy with that theory much of the operator algebra structure of
$C^*(\mathcal{Q})$
can be determined from
$\mathcal{Q}$
. We also show that many fundamental results from the theory of graph C*-algebras have natural analogues in the context of topological quivers (often with more involved proofs). These include the gauge-invariant uniqueness theorem, the Cuntz–Krieger uniqueness theorem, descriptions of the ideal structure, and conditions for simplicity.
Details
- Title: Subtitle
- TOPOLOGICAL QUIVERS
- Creators
- PAUL S MUHLY - Department of Mathematics, University of Iowa, Iowa City, IA 52242-1419, USAMARK TOMFORDE - Department of Mathematics, The College of William and Mary, P.O. Box 8795, Williamsburg, VA 23187-8795, USA
- Resource Type
- Journal article
- Publication Details
- International journal of mathematics, Vol.16(7), pp.693-755
- DOI
- 10.1142/S0129167X05003077
- ISSN
- 0129-167X
- eISSN
- 1793-6519
- Publisher
- World Scientific Publishing Company
- Language
- English
- Date published
- 08/2005
- Academic Unit
- Statistics and Actuarial Science; Mathematics
- Record Identifier
- 9984083893702771
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