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akadeemia kirjastus
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On the K-theory of the C*-algebra associated with a one-sided shift space; pp. 272–279

Full article in PDF format | doi: 10.3176/proc.2010.4.04

Authors
Toke Meier Carlsen, Sergei Silvestrov

Abstract
One-sided shift spaces are a special kind of non-invertible topological dynamical system with which one can associate a C*-algebra. We show how to construct the C*-algebra associated with a one-sided shift space as the Cuntz–Pimsner C*-algebra of a C*-correspondence and use this to compute its K-theory.
References

  1. Carlsen, T. M. Cuntz–Pimsner C*-algebras associated with subshifts. Internat. J. Math., 2008, 19, 47–70. MR 2380472.

  2. Carlsen, T. M. and Eilers, S. Matsumoto K-groups associated to certain shift spaces. Doc. Math., 2004, 9, 639–671. MR 2117431 (2005h:37021).

  3. Carlsen, T. M. and Matsumoto, K. Some remarks on the C*-algebras associated with subshifts. Math. Scand., 2004, 95, 145–160. MR 2091486 (2005e:46093).

  4. Carlsen, T. M. and Silvestrov, S. C*-crossed products and shift spaces. Expo. Math., 2007, 25, 275–307. MR 2360917.

  5. Exel, R. A new look at the crossed-product of a C*-algebra by an endomorphism. Ergodic Theory Dynam. Systems, 2003, 23, 1733–1750. MR 2032486 (2004k:46119).

  6. Katsura, T. On C*-algebras associated with C*-correspondences. J. Funct. Anal., 2004, 217, 366–401. MR 2102572 (2005e:46099).

  7. Kitchens, B. P. Symbolic Dynamics. Springer-Verlag, Berlin, 1998. MR 1484730.

  8. Lind, D. and Marcus, B. An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge, 1995. MR 1484730.

  9. Matsumoto, K. On C*-algebras associated with subshifts. Internat. J. Math., 1997, 8, 357–374. MR 1454478 (98h:46077).

10. Matsumoto, K. K-theory for C*-algebras associated with subshifts. Math. Scand., 1998, 82, 237–255. MR 1646513 (2000e:46087).

11. Matsumoto, K. Relations among generators of C*-algebras associated with subshifts. Internat. J. Math., 1999, 10, 385–405. MR 1688137 (2000f:46084).

12. Matsumoto, K. Dimension groups for subshifts and simplicity of the associated C*-algebras. J. Math. Soc. Japan, 1999, 51, 679–698. MR 1691469 (2000d:46082).

13. Matsumoto, K. Bowen–Franks groups for subshifts and Ext-groups for C*-algebras. K-Theory, 2001, 23, 67–104. MR 1852456 (2002h:19004).

14. Matsumoto, K. C*-algebras associated with presentations of subshifts. Doc. Math., 2002, 7, 1–30 (electronic). MR 1911208 (2004j:46083).
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