1Department of Mathematics Keio University Yokohama, 223-8522, Japan 2Department of Mathematics University of Iowa Iowa City, IA 52242-1419, U.S.A. 3School of Mathematics and Applied Statistics University of Wollongong Wollongong, NSW 2522, Australia 4Department of Mathematics University of Houston Houston, TX 77204-3008, U.S.A.
Studia Mathematica, Tome 187 (2008) no. 2, pp. 137-155
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.
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
Affiliations des auteurs :
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.
@article{10_4064_sm187_2_3,
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},
volume = {187},
number = {2},
doi = {10.4064/sm187-2-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm187-2-3/}
}
TY - JOUR
AU - Takeshi Katsura
AU - Paul S. Muhly
AU - Aidan Sims
AU - Mark Tomforde
TI - Ultragraph $C^*$-algebras via topological quivers
JO - Studia Mathematica
PY - 2008
SP - 137
EP - 155
VL - 187
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4064/sm187-2-3/
DO - 10.4064/sm187-2-3
LA - en
ID - 10_4064_sm187_2_3
ER -
%0 Journal Article
%A Takeshi Katsura
%A Paul S. Muhly
%A Aidan Sims
%A Mark Tomforde
%T Ultragraph $C^*$-algebras via topological quivers
%J Studia Mathematica
%D 2008
%P 137-155
%V 187
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/sm187-2-3/
%R 10.4064/sm187-2-3
%G en
%F 10_4064_sm187_2_3
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
