Explicit Construction and Uniqueness for Universal Operator Algebras of Directed Graphs |
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Authors: | Duncan Benton L |
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Institution: | Department of Mathematics, North Dakota State University Fargo, ND 58105, USA benton.duncan{at}ndsu.edu |
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Abstract: | Given a directed graph, there exist a universal operator algebraand universal C*-algebra associated to the directed graph. Inthis paper we give intrinsic constructions for these objects.We also provide an explicit construction for the maximal C*-algebraof an operator algebra. We discuss uniqueness of the universalalgebras for finite graphs, showing that for finite graphs thegraph is an isomorphism invariant for the universal operatoralgebra of a directed graph. We show that the underlying undirectedgraph is a Banach algebra isomorphism invariant for the universalC*-algebra of a directed graph. |
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