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EXPLICIT CONSTRUCTION AND UNIQUENESS FOR UNIVERSAL OPERATOR ALGEBRAS OF DIRECTED GRAPHS

Published online by Cambridge University Press:  08 December 2005

BENTON L. DUNCAN
BENTON L. DUNCAN
Affiliation:
Department of Mathematics, North Dakota State University, Fargo, ND 58105, USAbenton.duncan@ndsu.edu
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Abstract

Given a directed graph, there exist a universal operator algebra and universal $C^*$-algebra associated to the directed graph. In this paper we give intrinsic constructions for these objects. We also provide an explicit construction for the maximal $C^*$-algebra of an operator algebra. We discuss uniqueness of the universal algebras for finite graphs, showing that for finite graphs the graph is an isomorphism invariant for the universal operator algebra of a directed graph. We show that the underlying undirected graph is a Banach algebra isomorphism invariant for the universal $C^*$-algebra of a directed graph.

Keywords

47L40 (primary)47L55 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 72 , Issue 3 , December 2005 , pp. 763 - 778
Copyright
The London Mathematical Society 2005

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Footnotes

Part of this work was supported by US Department of Education grant #P200A030193.