A functorial approach to the C*-algebras of a graph

2001/02/28 by Jack Spielberg
Mathematics · #math.OA #msc:46L55

paper · pdf

published as International Journal of Math. v. 13 no. 3 (2002), 245-277. · 24 pages. See also http://math.la.asu.edu/~jss New version comments: Corrected typos, and added references

arxiv created 2001/10/05 · arxiv updated 2009/11/30

Abstract

A functor from the category of directed trees with inclusions to the category of commutative C*-algebras with injective *-homomorphisms is constructed. This is used to define a functor from the category of directed graphs with inclusions to the category of C*-algebras with injective *-homomorphisms. The resulting C*-algebras are identified as Toeplitz graph algebras. Graph algebras are proved to have inductive limit decompositions over any family of subgraphs with union equal to the whole graph. The construction is used to prove various structural properties of graph algebras.

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