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Type III factors arising from Cuntz-Krieger algebras

Author: Rui Okayasu
Journal: Proc. Amer. Math. Soc. 131 (2003), 2145-2153
MSC (2000): Primary 46L30
Published electronically: December 30, 2002
MathSciNet review: 1963761
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Abstract: We determine the types of factors arising from GNS-representations of quasi-free KMS states on Cuntz-Krieger algebras. Applying our result to the Cuntz-Krieger algebras arising from the boundary actions of some amalgamated free product groups, we also determine the types of harmonic measures on the boundaries.

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  • [Con] A. Connes, Une classification des facteurs de type III, (French) Ann. Sci. Ecole Norm. Sup. 6 (1973), 133-252. MR 49:5865
  • [Cun] J. Cuntz, Simple $C^\ast$-algebras generated by isometries, Commun. Math. Phys. 57 (1977), 173-185. MR 57:7189
  • [CK] J. Cuntz and W. Krieger, A class of $C^\ast$-algebras and topological Markov chains, Invent. Math. 56 (1980) 251-268. MR 82f:46073a
  • [EL] R. Exel and M. Laca, Partial Dynamical Systems and the KMS Condition, preprint (2000).
  • [EFW] M. Enomoto, M. Fujii and Y. Watatani, KMS states for gauge action on $\mathcal{O}\sb{A}$. Math. Japon. 29 (1984), no. 4, 607-619. MR 86b:46110
  • [Eva] D.E. Evans, On $\mathcal{O}_n$, Publ. Res. Inst. Math. Sci. 16 (1980), 915-927. MR 82g:46099
  • [Izu] M. Izumi, Subalgebras of infinite $C\sp *$-algebras with finite Watatani indices. I. Cuntz algebras, Comm. Math. Phys. 155 (1993), no. 1, 157-182. MR 94e:46104
  • [Kit] B.P. Kitchens, Symbolic dynamics. One-sided, two-sided and countable state Markov shifts, Universitext. Springer-Verlag, Berlin, 1998. MR 98k:58079
  • [Oka] R. Okayasu, Cuntz-Krieger-Pimsner algebras associated with amalgamated free product groups, Publ. Res. Inst. Math. Sci. 38 (2002), no. 1, 147-190.
  • [OP] D. Olesen and G.K. Pedersen, Some $C\sp{*} $-dynamical systems with a single KMS state, Math. Scand. 42 (1978), no. 1, 111-118. MR 80a:46041
  • [RR] J. Ramagge and G. Robertson, Factors from trees, Proc. Amer. Math. Soc. 125 (1997), no. 7, 2051-2055. MR 97i:46108
  • [Spi] J. Spielberg, Free product groups, Cuntz-Krieger algebras, and covariant maps, Internat. J. Math. 2 (1991) 457-476. MR 92j:46120
  • [SV] S. Stratila, and D. Voiculescu, Representations of AF-algebras and of the group $U(\infty )$, Lecture Notes in Mathematics, Vol. 486. Springer-Verlag, Berlin-New York, 1975. viii+169 pp. MR 56:16391

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Additional Information

Rui Okayasu
Affiliation: Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan

Received by editor(s): September 27, 2001
Received by editor(s) in revised form: February 19, 2002
Published electronically: December 30, 2002
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society

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