Explicit construction and uniqueness for universal operator algebras of directed graphs

Details Explicit construction and uniqueness for universal operator algebras of directed graphs Explicit construction and uniqueness for universal operator algebras of directed graphs

2004-10-12

arxiv.org/abs/math/0410290v2

J. London Math. Soc. 72 (2005) 763-778

Mathematics

Operator Algebras

16 pages, uses xy-pic

Scientific paper

Given a directed graph, there exists a universal operator algebra and universal C*-algebra associated to the directed graph. In this paper we give intrinsic constructions of these objects. We provide an explicit construction for the maximal C*-algebra of an operator algebra. We also 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.

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