No Access

The prime spectrum and primitive ideal space of a graph C*-algebra

Gene Abrams

Department of Mathematics, University of Colorado, Colorado Springs, CO 80918, USA

Search for more papers by this author

and

Mark Tomforde

Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA

Search for more papers by this author

https://doi.org/10.1142/S0129167X14500700Cited by:0 (Source: Crossref)

Abstract

We describe primitive and prime ideals in the C*-algebra C*(E) of a graph E satisfying Condition (K), together with the topologies on each of these spaces. In particular, we find that primitive ideals correspond to the set of maximal tails disjoint union the set of finite-return vertices, and that prime ideals correspond to the set of clusters of maximal tails disjoint union the set of finite-return vertices.

Keywords:

AMSC: 46L55

References

G. Abrams and M. Tomforde, A class of C* -algebras that are prime but not primitive, to appear in Münster J. Math . Google Scholar
T. Bateset al., Illinois J. Math. 46(4), 1159 (2002). Crossref, Web of Science, Google Scholar
T. Bates et al. , New York J. Math. 6 , 307 ( 2000 ) . Google Scholar
J. Dixmier , Bull. Soc. Math France 88 , 95 ( 1960 ) . Crossref, Google Scholar
J. G. Hocking and G. S. Young , Topology , 2nd edn. ( Dover Publications , New York , 1988 ) . Google Scholar
J. H. Hong and W. Szymański , J. Math. Soc. Japan 56 , 45 ( 2004 ) . Crossref, Web of Science, Google Scholar
T. Katsura , Trans. Amer. Math. Soc. 356 , 4287 ( 2004 ) . Crossref, Web of Science, Google Scholar
T. Katsura , Ergodic Theory Dynam. Systems 26 , 1805 ( 2006 ) . Crossref, Web of Science, Google Scholar
G. J. Murphy , C* -Algebras and Operator Theory ( Academic Press , Boston, MA , 1990 ) . Google Scholar
I. Raeburn and D. P. Williams , Morita Equivalence and Continuous-Trace C* -Algebras , Mathematical Surveys and Monographs 60 ( American Mathematical Society , Providence, RI , 1998 ) . Crossref, Google Scholar
K. M. Rangaswamy , J. Algebra 375 , 73 ( 2013 ) . Crossref, Web of Science, Google Scholar
M. Tomforde , Graph Algebras: Bridging the Gap Between Analysis and Algebra , eds. G. A. Pino , F. P. Domènech and M. S. Molina ( Servicio de Publicaciones de la Universidad de Málaga , Málaga , 2006 ) . Google Scholar
N. Weaver , J. Funct. Anal. 203 , 356 ( 2003 ) . Crossref, Web of Science, Google Scholar