Higher rank graph C*-algebras

New York Journal of Mathematics

Volumn 6, Issue , 2000, Pages 1-20

  Kumjian, Alex ^a   Pask, David ^b  

^a UNIVERSITY OF NEVADA   (United States)

^b UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

C* algebra; Graph algebra; Graphs as categories; Path groupoid

Indexed keywords

EID: 0001872445     PISSN: 10769803     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. C. Anantharaman-Delaroche, Purely infinite C*-algebras arising from dynamical systems, Bull. Soc. Math. France 125 (1997), 199-225, MR 99i:46051, Zbl 896.46044.
2. C. Anantharaman-Delaroche and J. Renault, Amenable groupoids, To appear.
3. S. Adji, M. Laca, M. Nilsen and I. Raeburn, Crossed products by semigroups of endomorphisms and the Toeplitz algebras of ordered groups, Proc. Amer Math. Soc. 122 (1994), 1133-1141, MR 95b:46094, Zbl 818.46071.
4. T. Bates, D. Pask, I. Raeburn, W. Szymanski, The C*-algebras of row-finite graphs, Submitted.
5. O. Bratteli, Inductive limits of finite dimensional C*-algebras, Trans. Amer. Math. Soc. 171 (1972), 195-234, MR 47 #844, Zbl 264.46057.
6. J. Cuntz and W. Krieger, A class of C*-algebras and topological Markov chains, Invent. Math. 56 (1980), 251-268, MR 82f:46073a, Zbl 434.46045.
7. V. Deaconu, Groupoids associated with endomorphisms, Trans. Amer. Math. Soc. 347 (1995), 1779-1786, MR 95h:46104, Zbl 826.46058.
8. J. L. Gross and T. W. Tucker, Topological Graph Theory, Wiley Interscience Series in Discrete Mathematics and Optimization, Wiley, New York, 1987, MR 88h:05034 Zbl 621.05013.
9. P. J. Higgins, Notes on Categories and Groupoids, van Nostrand Rienhold, London, 1971, MR 48 #6288, Zbl 226.20054.
10. A. an Huef and I. Raeburn, The ideal structure of Cuntz-Krieger algebras, Ergod. Th. and Dyn. Sys. 17 (1997), 611-624, MR 98k:46098, Zbl 886.46061.
11. S. Kaliszewski, J. Quigg and I. Raeburn, Skew products and crossed products by coactions, Preprint.
12. E. Kirchberg The classification of purely infinite C*-algebras using Kasparov's theory, Preprint.
13. A. Kumjian, D. Pask, I. Raeburn, and J. Renault, Graphs, groupoids and Cuntz-Krieger algebras, J. Funct. Anal. 144 (1997), 505-541, MR 98g:46083.
14. A. Kumjian, D. Pask, I. Raeburn, Cuntz-Krieger algebras of directed graphs, Pacific. J. Math. 184 (1998), 161-174, MR 99i:46049, Zbl 917.46056.
15. A. Kumjian and D. Pask, C*-algebras of directed graphs and group actions, Ergod. Th. & Dyn. Sys., to appear.
16. M. Laca and J. Spielberg, Purely infinite C*-algebras from boundary actions of discrete groups, J. Reine Angew. Math. 480 (1996), 125-139, MR 98a:46085, Zbl 863.46044.
17. S. MacLane, Categories for the Working Mathematician, Graduate Texts in Mathematics, no. 5, Springer-Verlag, Berlin, 1971 MR 50 #7275, Zbl 906.18001.
18. T. Masuda, Groupoid dynamical systems and crossed product II - the case of C*-systems, Publ. RIMS Kyoto Univ. 20 (1984), 959-970, MR 86g:46100, Zbl 584.46056.
19. P. Muhly, A finite dimensional introduction to operator algebra, In Operator Algebras and Applications (Samos, 1996), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., no. 495, Kluwer Acad. Publ., Dordrecht, 1997, 313-354, MR 98h:46062, Zbl 908.47046.
20. N. C. Phillips, A classification theorem for nuclear purely infinite simple C*-algebras, Preprint.
21. J. Renault, A Groupoid Approach to C*-Algebras, Lecture Notes in Mathematics, no. 793, Springer-Verlag, Berlin, 1980, MR 82h:46075, Zbl 433.46049.
22. G. Robertson and T. Steger, C*-algebras arising from group actions on the boundary of a triangle building, Proc. London Math. Soc. 72 (1996), 613-637, MR 98b:46088, Zbl 869.46035.
23. G. Robertson and T. Steger, Affine buildings, tiling systems and higher rank Cuntz-Krieger algebras, J. Reine Angew. Math. 513 (1999), 115-144.
24. G. Robertson and T. Steger, K-theory for rank two Cuntz-Krieger algebras, Preprint.
25. J. Rosenberg and C. Schochet, The Künneth theorem and the universal coefficient theorem for Kasparov's generalized K-functor, Duke Math. J. 55 (1987), 431-474, MR 88i:46091, Zbl 644.46051.