Geodesic
Ultragraph $C^*$-algebras via topological quivers
Takeshi Katsura 1   ; Paul S. Muhly 2   ; Aidan Sims 3   ; Mark Tomforde 4
1 Department of Mathematics Keio University Yokohama, 223-8522, Japan
2 Department of Mathematics University of Iowa Iowa City, IA 52242-1419, U.S.A.
3 School of Mathematics and Applied Statistics University of Wollongong Wollongong, NSW 2522, Australia
4 Department of Mathematics University of Houston Houston, TX 77204-3008, U.S.A.
Studia Mathematica, Tome 187 (2008) no. 2, pp. 137-155 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Given an ultragraph in the sense of Tomforde, we construct a topological quiver in the sense of Muhly and Tomforde in such a way that the universal $C^*$-algebras associated to the two objects coincide. We apply results of Muhly and Tomforde for topological quiver algebras and of Katsura for topological graph $C^*$-algebras to study the $K$-theory and gauge-invariant ideal structure of ultragraph $C^*$-algebras.
DOI : 10.4064/sm187-2-3
Keywords: given ultragraph sense tomforde construct topological quiver sense muhly tomforde universal * algebras associated objects coincide apply results muhly tomforde topological quiver algebras katsura topological graph * algebras study k theory gauge invariant ideal structure ultragraph * algebras

Takeshi Katsura  1   ; Paul S. Muhly  2   ; Aidan Sims  3   ; Mark Tomforde  4

1 Department of Mathematics Keio University Yokohama, 223-8522, Japan
2 Department of Mathematics University of Iowa Iowa City, IA 52242-1419, U.S.A.
3 School of Mathematics and Applied Statistics University of Wollongong Wollongong, NSW 2522, Australia
4 Department of Mathematics University of Houston Houston, TX 77204-3008, U.S.A. 
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     author = {Takeshi Katsura and Paul S. Muhly and Aidan Sims and Mark Tomforde},
     title = {Ultragraph $C^*$-algebras via topological quivers},
     journal = {Studia Mathematica},
     pages = {137--155},
     year = {2008},
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Takeshi Katsura; Paul S. Muhly; Aidan Sims; Mark Tomforde. Ultragraph $C^*$-algebras via topological quivers. Studia Mathematica, Tome 187 (2008) no. 2, pp. 137-155. doi: 10.4064/sm187-2-3

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