Affine buildings, tiling systems and higher rank Cuntz-Krieger algebras

Journal fur die Reine und Angewandte Mathematik

Volumn 513, Issue , 1999, Pages 115-144

  Robertson, Guyan ^a   Steger, Tim ^b  

^a UNIVERSITY OF NEWCASTLE   (Australia)

^b UNIVERSITY OF SASSARI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033240618     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: 10.1515/crll.1999.057     Document Type: Article

References (28)

1. C. Anantharaman-Delaroche. Systèmes dynamiques non commutatifs et moyennabilité, Math. Ann. 279 (1987), 297-315.
2. B. Blackadar, K-theory for Operator Algebras, Second Edition, MSRI Publ. 5, Cambridge University Press, Cambridge 1998.
3. K. Brown, Buildings, Springer-Verlag, New York 1989.
4. K. Brown, Five lectures on buildings, Group Theory from a Geometrical Viewpoint (Trieste 1990), World Sci. Publishing, River Edge, N.J. (1991), 254-295.
5. M. Burger and S. Mozes, Finitely presented groups and products of trees, C.R. Acad. Sci. Paris (1) 324 (1997), 747-752.
6. D.I. Cartwright, A brief introduction to buildings, Harmonic Functions on Trees and Buildings (New York 1995), Contemp. Math. 206. Amer. Math. Soc. (1997), 45-77.
7. D.I. Cartwright, A brief introduction to buildings, Harmonic Functions on Trees and Buildings (New York 1995), Contemp. Math. 206. Amer. Math. Soc. (1997), 45-77.
8. 2 groups, Ann. Inst. Fourier 44 (1993), 213-248.
9. 2, I and II, Geom. Ded. 47 (1993), 143-166 and 167-223.
10. J. Cuntz, A class of C*-algebras and topological Markov chains: Reducible chains and the Ext-functor for C*-algebras, Invent. Math. 63 (1981), 23-50.
11. J. Cuntz, K-theory for certain C*-algebras, Ann. Math. 113 (1981), 181-197.
12. J. Cuntz and W. Krieger, A class of C*-algebras and topological Markov chains, Invent. Math. 56 (1980), 251-268.
13. P. Garrett, Buildings and Classical Groups, Chapman & Hall, London 1997.
14. R.V. Kadison and J.R. Ringrose, Fundamentals of the Theory of Operator Algebras, Volume II, Academic Press, New York 1986.
15. E. Kirchberg, Exact C*-algebras, tensor products, and the classification of purely infinite algebras, Proc. Intern. Congr. Math. (Zürich 1994). Vol.2, Birkhäuser, Basel (1995), 943-954.
16. E. Kirchberg, The classification of purely infinite C*-algebras using Kasparov's theory, in: Lectures in Operator Algebras, Fields Institute Monographs, Amer. Math. Soc., 1998.
17. S. Mozes, Actions of Cartan subgroups, Israel J. Math. 90 (1995), 253-294.
18. S. Mozes, A zero entropy, mixing of all orders tiling system, Contemp. Math. 135 (1992), 319-325.
19. G.K. Pedersen, C*-algebras and their Automorphism Groups, Academic Press, New York 1979.
20. N.C. Phillips, A classification theorem for purely infinite simple C*-algebras, preprint, Oregon 1995.
21. J.C. Quigg and J. Spielberg, Regularity and hyporegularity in C*-dynamical systems, Houston J. Math. 18 (1992), 139-152.
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.
23. G. Robertson and T. Steger, K-theory for rank two Cuntz-Krieger algebras, preprint.
24. M. Ronan, Lectures on Buildings, Perspect. Math. 7, Academic Press, New York 1989.
25. J. Spielberg, Free product groups, Cuntz-Krieger algebras, and covariant maps, Intern. J. Math. 2 (1991), 457-476.
26. T. Steger, Local fields and buildings, Harmonic Functions on Trees and Buildings (New York 1995), Contemp. Math. 206, Amer. Math. Soc. (1997), 79-107.
27. T. Steger, Local fields and buildings, Harmonic Functions on Trees and Buildings (New York 1995), Contemp. Math. 206, Amer. Math. Soc. (1997), 79-107.
28. R.J. Zimmer, Ergodic Theory and Semisimple Groups, Birkhäuser, Boston 1984.