### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 245-277 |

Number of pages | 33 |

Journal | International Journal of Mathematics |

Volume | 13 |

Issue number | 3 |

DOIs | |

State | Published - May 2002 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**A functorial approach to the C*-algebras of a graph.** / Spielberg, John.

Research output: Contribution to journal › Article

*International Journal of Mathematics*, vol. 13, no. 3, pp. 245-277. https://doi.org/10.1142/S0129167X02001319

}

TY - JOUR

T1 - A functorial approach to the C*-algebras of a graph

AU - Spielberg, John

PY - 2002/5

Y1 - 2002/5

N2 - 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.

AB - 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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UR - http://www.scopus.com/inward/citedby.url?scp=0036082894&partnerID=8YFLogxK

U2 - 10.1142/S0129167X02001319

DO - 10.1142/S0129167X02001319

M3 - Article

AN - SCOPUS:0036082894

VL - 13

SP - 245

EP - 277

JO - International Journal of Mathematics

JF - International Journal of Mathematics

SN - 0129-167X

IS - 3

ER -