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Classification theorems for the C*-Algebras of graphs with sinks

Published online by Cambridge University Press:  17 April 2009

Iain Raeburn ,
Mark Tomforde  and
Dana P. Williams
Iain Raeburn
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia, e-mail: [email protected]
Mark Tomforde
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States of America, e-mail: [email protected]
Dana P. Williams
Affiliation:
Department of Mathematics, Dartmouth College, Hanover, NH 03755, United States of America e-mail: [email protected]
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We consider graphs E which have been obtained by adding one or more sinks to a fixed directed graph G. We classify the C*-algebra of E up to a very strong equivalence relation, which insists, loosely speaking, that C*(G) is kept fixed. The main invariants are vectors WE: G0 → ℕ which describe how the sinks are attached to G; more precisely, the invariants are the classes of the WE in the cokernel of the map A – I, where A is the adjacency matrix of the graph G.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 1 , August 2004 , pp. 143 - 161
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Bates, T., Pask, D., Raeburn, I. and Syzmański, W., ‘The C *-algebras of row-finite graphs’, New York J. Math. 6 (2000), 307–324.Google Scholar
[2]Cuntz, J. and Krieger, W., ‘A class of C *-algebras and topological Markov chains’, Invent. Math. 56 (1980), 251–268.CrossRefGoogle Scholar
[3]Exel, R. and Laca, M., ‘Cuntz-Krieger algebras for infinite matrices’, J. reine angew. Math. 512 (1999), 119–172.CrossRefGoogle Scholar
[4]Huang, D., ‘Flow equivalence of reducible shifts of finite type and Cuntz-Krieger algebras’, J. reine angew. Math. 462 (1995), 185–217.Google Scholar
[5]Kumjian, A., Pask, D. and Raeburn, I., ‘Cuntz-Krieger algebras of directed graphs’, Pacific J. Math. 184 (1998), 161–174.CrossRefGoogle Scholar
[6]Kumjian, A., Pask, D., Raeburn, I. and Renault, J., ‘Graphs, groupoids, and Cuntz-Krieger algebras’, J. Funct. Anal. 144 (1997), 505–541.CrossRefGoogle Scholar
[7]Lind, D. and Marcus, B., An Introduction to symbolic dynamics and coding (Cambridge Univ. Press, Cambridge, 1995).CrossRefGoogle Scholar
[8]Paschke, W.L., ‘K-theory for actions of the circle group on C *-algebras’, J. Operator Theory 6 (1981), 125–133.Google Scholar
[9]Raeburn, I., ‘On crosse products and Takai duality’, Proc. Edinburgh Math. Soc. 31 (1988), 321–330.CrossRefGoogle Scholar
[10]Raeburn, I. and Szymański, W., ‘Cuntz-Krieger algebras of infinite graphs and matrices’, Trans. Amer. Math. Soc. 356 (2004), 39–59.CrossRefGoogle Scholar
[11]Rordam, Y., ‘Classification of Cuntz-Krieger algebras’, K-theory 9 (1995), 31–58.CrossRefGoogle Scholar
[12]Watatani, Y., ‘Graph theory for C *-algebras’, in Operator Algebras and Their Applications, (Kadison, R.V., Editor), Proc. Sympos. Pure Math. 38 (Amer. Math. Soc. Providence, R.I., 1982), pp. 195–197.CrossRefGoogle Scholar