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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 579042, 7 pages
-Algebras from Groupoids on Self-Similar Groups
Department of Mathematics Education, Ewha Womans University, Seoul 120-750, Republic of Korea
Received 10 May 2013; Accepted 2 July 2013
Academic Editor: Salvador Hernandez
Copyright © 2013 Inhyeop Yi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- V. Nekrashevych, Self-Similar Groups, vol. 117 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 2005.
- V. Nekrashevych, “-algebras and self-similar groups,” Journal für die Reine und Angewandte Mathematik, vol. 630, pp. 59–123, 2009.
- I. F. Putnam, “-algebras from Smale spaces,” Canadian Journal of Mathematics, vol. 48, no. 1, pp. 175–195, 1996.
- I. Putnam, Hyperbolic Systems and Generalized Cuntz-Krieger Algebras, Lecture notes from Summer School in Operator Algebras, Odense, Denmark, 1996.
- I. F. Putnam and J. Spielberg, “The structure of -algebras associated with hyperbolic dynamical systems,” Journal of Functional Analysis, vol. 163, no. 2, pp. 279–299, 1999.
- D. Ruelle, Thermodynamic Formalism, vol. 5, Addison-Wesley, 1978.
- D. Ruelle, “Noncommutative algebras for hyperbolic diffeomorphisms,” Inventiones Mathematicae, vol. 93, no. 1, pp. 1–13, 1988.
- C. Anantharaman-Delaroche, “Purely infinite -algebras arising from dynamical systems,” Bulletin de la Société Mathématique de France, vol. 125, no. 2, pp. 199–225, 1997.
- V. Deaconu, “Groupoids associated with endomorphisms,” Transactions of the American Mathematical Society, vol. 347, no. 5, pp. 1779–1786, 1995.
- P. S. Muhly, J. N. Renault, and D. P. Williams, “Equivalence and isomorphism for groupoid -algebras,” Journal of Operator Theory, vol. 17, no. 1, pp. 3–22, 1987.
- X. Chen and C. Hou, “Morita equivalence of groupoid -algebras arising from dynamical systems,” Studia Mathematica, vol. 149, no. 2, pp. 121–132, 2002.
- J. Renault, “Cuntz-like algebras,” in Operator Theoretical Methods, pp. 371–386, Bucharest, Romania, Theta Foundation, 2000.
- A. Kumjian and D. Pask, “Actions of associated to higher rank graphs,” Ergodic Theory and Dynamical Systems, vol. 23, no. 4, pp. 1153–1172, 2003.
- G. A. Elliott, G. Gong, and L. Li, “Approximate divisibility of simple inductive limit -algebras,” Contemporary Mathematics, vol. 228, pp. 87–97, 1998.
- J. Renault, A Groupoid Approach to C∗-Algebras, vol. 793 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1980.
- S. Zhang, “Certain -algebras with real rank zero and their corona and multiplier algebras. I,” Pacific Journal of Mathematics, vol. 155, no. 1, pp. 169–197, 1992.
- J.-L. Tu, “La conjecture de Baum-Connes pour les feuilletages moyennables,” K-Theory in the Mathematical Sciences, vol. 17, no. 3, pp. 215–264, 1999.
- J. Renault, “The Radon-Nikodym problem for appoximately proper equivalence relations,” Ergodic Theory and Dynamical Systems, vol. 25, no. 5, pp. 1643–1672, 2005.
- A. Kumjian and J. Renault, “KMS states on -algebras associated to expansive maps,” Proceedings of the American Mathematical Society, vol. 134, no. 7, pp. 2067–2078, 2006.
- P. S. Muhly and D. P. Williams, “Continuous trace groupoid -algebras,” Mathematica Scandinavica, vol. 66, no. 2, pp. 231–241, 1990.
- A. An Huef, I. Raeburn, and D. P. Williams, “Properties preserved under Morita equivalence of -algebras,” Proceedings of the American Mathematical Society, vol. 135, no. 5, pp. 1495–1503, 2007.
- K. Thomsen, “-algebras of homoclinic and heteroclinic structure in expansive dynamics,” Memoirs of the American Mathematical Society, vol. 206, no. 970, 2010.
- G. Gong, “On the classification of simple inductive limit -algebras—I. The reduction theorem,” Documenta Mathematica, vol. 7, pp. 255–461, 2002.
- B. Blackadar, A. Kumjian, and M. Rørdam, “Approximately central matrix units and the structure of noncommutative tori,” K-Theory, vol. 6, no. 3, pp. 267–284, 1992.