The noncommutative geometry of graph C*-algebras I: The index theorem

Journal of Functional Analysis

Volumn 233, Issue 1, 2006, Pages 92-134

  Pask, David ^a   Rennie, Adam ^a  

^a UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

Graph C* algebra; Index theorem; K theory; KK theory; Semifinite von Neumann algebra; Spectral triple; Trace

Indexed keywords

EID: 32544449019     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2005.07.009     Document Type: Article

References (35)

1. A. An Huef Honours Thesis 1994 University of Newcastle
2. T. Bates D. Pask I. Raeburn W. Szymanski The C*-algebras of row-finite graphs New York J. Math. 6 2000 307-324
3. O. Bratteli, D. Robinson, Operator Algebras and Quantum Statistical Mechanics, vol. 1, second ed., Springer, Berlin, 1987.
4. A. Carey J. Phillips A. Rennie F. Sukochev The Hochschild class of the chern character of semifinite spectral triples J. Funct. Anal. 213 2004 111-153
5. A. Carey, J. Phillips, A. Rennie, F. Sukochev, The local index theorem in semifinite von Neumann algebras I: Spectral flow, Adv. Math., to appear.
6. A. Carey, J. Phillips, A. Rennie, F. Sukochev, The local index theorem in semifinite von Neumann algebras II: The even case, Adv. Math. to appear.
7. A. Carey J. Phillips F. Sukochev Spectral flow and dixmier traces Adv. Math. 173 2003 68-113
8. A. Connes Noncommutative Geometry 1994 Academic Press New York
9. A. Connes H. Moscovici The local index formula in noncommutative geometry GAFA 5 1995 174-243
10. K. Deike J.H. Hong W. Szymanski Stable rank of graph algebras Type I graph algebras and their limits Indiana Univ. Math. J. 52 4 2003 963-979
11. J. Dixmier Von Neumann Algebras 1981 North-Holland Amsterdam
12. T. Fack H. Kosaki Generalised s-numbers of τ-measurable operators Pacific J. Math. 123 1986 269-300
13. V. Gayral J.M. Gracia-Bondía B. Iochum T. Schücker J.C. Varilly Moyal planes are spectral triples Comm. Math. Phys. 246 2004 569-623
14. J.M. Gracia-Bondía J.C. Varilly H. Figueroa Elements of Non-commutative Geometry 2001 Birkhauser Boston
15. N. Higson, The local index formula in noncommutative geometry, Contemporary developments in Algebraic K-Theory, ictp Lecture Notes, No. 15, 2003, pp. 444-536.
16. N. Higson J. Roe Analytic K-Homology 2000 Oxford University Press Oxford
17. J.V.B. Hjelmborg Purely infinite and stable C*-algebras of graphs and dynamical systems Ergod. Theory Dynam. Systems 21 2001 1789-1808
18. R.V. Kadison J.R. Ringrose Fundamentals of the Theory of Operator Algebras vol II: Advanced Theory 1986 Academic Press New York
19. G.G. Kasparov The operator K-functor and extensions of C*-algebras Math. USSR. Izv. 16 3 1981 513-572
20. A. Kumjian D. Pask I. Raeburn J. Renault Graphs, groupoids and Cuntz-Krieger algebras J. Funct. Anal. 144 1997 505-541
21. A. Kumjian D. Pask I. Raeburn Cuntz-Krieger algebras of directed graphs Pacific J. Math. 184 1998 161-174
22. E.C. Lance Hilbert C*-modules 1995 Cambridge University Press Cambridge
23. A. Mallios Topological Algebras, Selected Topics 1986 Elsevier Science Publishers B.V. Amsterdam
24. D. Pask, I. Raeburn, On the K-Theory of Cuntz-Krieger algebras, Publ. RIMS Kyoto University vol. 32 (3), 1996, pp. 415-443.
25. D. Pask, A. Rennie, One dimensional noncommutative manifolds from graph C*-algebras, in preparation.
26. J. Phillips I. Raeburn An index theorem for Toeplitz operators with noncommutative symbol space J. Funct. Anal. 120 2 1994 239-263
27. I. Raeburn, Graph algebras: C*-algebras we can see, CBMS Lecture Notes, to appear.
28. I. Raeburn W. Szymanski Cuntz-Krieger algebras of infinite graphs and matrices Trans. Amer. Math. Soc. 356 1 2004 39-59
29. I. Raeburn D.P. Williams Morita equivalence and continuous-trace C*-Algebras Math. Surveys Monographs 60 1998
30. A. Rennie Smoothness and locality for nonunital spectral triples K-Theory 28 2 2003 127-165
31. A. Rennie Summability for nonunital spectral triples K-Theory 31 2004 71-100
32. M. Rørdam, F. Larsen, N.J. Laustsen, An Introduction to K-Theory and C*-Algebras, LMS Student Texts, vol. 49, CUP, 2000.
33. n (A) is local if A is Local and Fréchet Internat. J. Math. 3 4 1992 581-589
34. S. Stratila L. Zsidó Lectures on von Neumann Algebras 1975 Abacus Press
35. M. Tomforde, Real Rank Zero and Tracial States of C*-Algerbras Associated to Graphs, math. OA/0204095 v2.