Cohomology of topological graphs and Cuntz-Pimsner algebras

Journal of Operator Theory

Volumn 46, Issue 2, 2001, Pages 251-264

  Deaconu, V ^a   Kumjian, A ^a   Muhly, P ^b  

^a UNIVERSITY OF NEVADA   (United States)

^b UNIVERSITY OF IOWA   (United States)

Author keywords

And C* correspondence; Cuntz Pimsner algebras; Groupoid cohomology; Hilbert bimodules; Hilbert modules

Indexed keywords

EID: 0039890481     PISSN: 03794024     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. B. ABADIE, S, EILERS, R. EXEL, Morita equivalence for crossed products by Hubert C*-bimodules, Trans. Amer. Math. Soc. 350(1998), 3043-3054.
2. C. ANANTHARAMAN-DELAROCHE, Purely infinite C*-algebras arising from dynamical systems, Bull. Soc. Math. France 125(1997), 199-225.
3. V. ARZUMANIAN, J. RENAULT, Examples of pseudogroups and their C*-algebras, in Operator Algebras and Quantum Field Theory, S. Doplicher, R. Longo, J.E. Roberts, and L. Zsido editors, International Press, Cambridge, Mass, 1997, pp. 93-104.
4. B. BRENKEN, The local product structure of expansive automorphisms of solenoids and their associated C*-algebras, Canad. J. Math. 48(1996), 692-709.
5. V. DEACONU, Groupoids associated with endomorphisms, Trans. Amer. Math. Soc. 347(1995), 1779-1786.
6. V. DEACONU, Generalized solenoids and C*-algebras, Pacific J. Math. 190(1999), 247-260.
7. S. EILENBERG, N. STEENROD, Foundations of Algebraic Topology, Princeton University Press, 1952.
8. N. FOWLER, P. MUHLY, I. RAEBURN, Representations of Cuntz-Pimsner algebras, Indiana Math. J., to appear.
9. A. GROTHENDIECK, Sur quelques points d'algèbre homologique, Tôhoku Math. J. 9(1957), 119-221.
10. B. IVERSEN, Cohomology of Sheaves, Universitext, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo 1986.
11. A. KISHIMOTO, Simple crossed products by locally compact abelian groups, Yokohama Math. J. 28(1980), 69-85.
12. A. KISHIMOTO, A. KUMJIAN, Simple stably projectionless C*-algebras arising as crossed products, Canad. J. Math. 48(1996), 980-996.
13. A. KUMJIAN, Diagonals in algebras of continuous trace, in Operator algebras and their connections with topology and ergodic theory, Lecture Notes in Math., vol. 1132, Springer-Verlag, Berlin-Heidelberg-New York 1985, pp. 297-311.
14. A. KUMJIAN, On C*-diagonals, Canad. J. Math. 38(1986), 969-1008.
15. A. KUMJIAN, On equivariant sheaf cohomology and elementary C*-bundles, J. Operator Theory 10(1988), 207-240.
16. A. KUMJIAN, P. MUHLY, J. RENAULT, D. WILLIAMS, The Brauer group of a locally compact groupoid, Amer. J. Math. 120(1998), 901-954.
17. A. KUMJIAN, D. PASK, C*-algebras of directed graphs and group actions, Ergodic Theory Dynamical Systems 19(1999), 1503-1519.
18. A. KUMJIAN, D. PASK, I. RAEBURN, Cuntz-Krieger algebras of directed graphs, Pacific J. Math. 184(1998), 161-174.
19. P. MUHLY, B. SOLEL, Tensor algebras over C*-correspondences (Representations and C*-envelopes), J. Funct. Anal. 158(1998), 389-457.
20. P. MUHLY, B. SOLEL, On the simplicity of some Cuntz-Pimsner algebras, Math. Scand. 83(1998), 53-73.
21. J. PHILLIPS, I. RAEBURN, Automorphisms of C*-algebras and second Čech cohomology, Indiana Math. J. 29(1980), 799-822.
22. M. PIMSNER, A class of C*-algebras generalizing both Cuntz-Krieger algebras and crossed products by ℤ, in Free probability theory, D. Voiculescu, Ed., Fields Inst. Commun., vol. 12, Amer. Math. Soc., Providence 1997, pp. 189-212.
23. J. RENAULT, A groupoid approach to C*-algebras, Lecture Notes in Math., vol. 793, Springer-Verlag, Berlin-Heidelberg-New York 1980.
24. M. RIEFFEL, Induced representations of C*-algebras, Adv. in Math. 13(1974), 176-257.
25. B. TENNISON, Sheaf theory, London Math. Soc. Lecture Note Ser., vol. 20, Cambridge University Press, Cambridge-London-New York-Melbourne 1975.