Acta Mathematica

, 189:1 | Cite as

Topological entropy of free product automorphisms

  • N. P. Brown
  • K. Dykema
  • D. Shlyakhtenko


Entropy Free Product Topological Entropy Product Automorphism 
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  1. [1]
    Arveson, W., Notes on extensions ofC *-algebras.Duke Math. J., 44 (1977), 329–355.CrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    Berg, K. R., convolution of invariant measures, maximal entropy.Math. Systems Theory, 3 (1969), 146–150.CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    Blackadar, B.,K-theory for Operator Algebras. Math. Sci. Res. Inst. Publ., 5. Springer-Verlag, New York, 1986.MATHGoogle Scholar
  4. [4]
    Blanchard, E. &Dykema, K., Embeddings of reduced free products of operator algebras.Pacific J. Math., 199 (2001), 1–19.MathSciNetMATHGoogle Scholar
  5. [5]
    Boca, F. P. &Goldstein, P., Topological entropy for the canonical endomorphism on Cuntz-Krieger algebras.Bull. London Math. Soc., 32 (2000), 345–352.CrossRefMathSciNetMATHGoogle Scholar
  6. [6]
    Boyle, M. &Handleman, D., Entropy versus orbit equivalence for minimal homeomorphisms.Pacific J. Math., 164 (1994), 1–13.MathSciNetMATHGoogle Scholar
  7. [7]
    Brown, N. P., Topological entropy in exactC *-algebras.Math. Ann., 314 (1999), 347–367.CrossRefMATHMathSciNetGoogle Scholar
  8. [8]
    Brown, N. P. &Choda, M., Approximation entropies in crossed products with an application to free shifts.Pacific J. Math., 198 (2001), 331–346.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    Brown, N. P. &Germain, E., Dual entropy in discrete groups with amenable actions.Ergodic Theory Dynam. Systems, 22 (2002), 711–728.CrossRefMathSciNetMATHGoogle Scholar
  10. [10]
    Choda, M., Entropy of Cuntz's canonical endomorphism.Pacific J. Math., 190 (1999), 235–245.MATHMathSciNetGoogle Scholar
  11. [11]
    Choda, M. &Dykema, K., Purely infinite, simpleC *-algebras arising from free product constructions, III.Proc. Amer. Math. Soc., 128 (2000), 3269–3273.CrossRefMathSciNetMATHGoogle Scholar
  12. [12]
    Connes, A., Narnhofer, H. &Thirring, W., Dynamical entropy ofC *-algebras and von Neumann algebras.Comm. Math. Phys., 112 (1987), 691–719.CrossRefMathSciNetMATHGoogle Scholar
  13. [13]
    Connes, A. &Størmer, E., Entropy for automorphisms of II1 von Neumann algebras.Acta Math., 134 (1975), 289–306.MathSciNetMATHGoogle Scholar
  14. [14]
    Cuntz, J., SimpleC *-algebras generated by isometries.Comm. Math. Phys., 57 (1977), 173–185.CrossRefMATHMathSciNetGoogle Scholar
  15. [15]
    —,K-theory for certainC *-algebras.Ann. of Math., (2), 113 (1981), 181–197.CrossRefMATHMathSciNetGoogle Scholar
  16. [16]
    Dykema, K., Simplicity and the stable rank of some free productC *-algebras.Trans. Amer. Math. Soc., 351 (1999), 1–40.CrossRefMATHMathSciNetGoogle Scholar
  17. [17]
    —, Topological entropy of some automorphisms of reduced amalgamated free productC *-algebras.Ergodic Theory Dynam. Systems, 21 (2001), 1683–1693.MATHMathSciNetCrossRefGoogle Scholar
  18. [18]
    —, Purely infinite, simpleC *-algebras arising from free product constructions, II.Math. Scand., 90 (2002), 73–86.MATHMathSciNetGoogle Scholar
  19. [19]
    Dykema, K., Exactness of reduced amalgamated free productC *-algebras. To appear inForum Math.Google Scholar
  20. [20]
    Dykema, K. &Shlyakhtenko, D., Exactness of Cuntz-PimsnerC *-algebras.Proc. Edinb. Math. Soc. (2), 44 (2001), 425–444.CrossRefMathSciNetMATHGoogle Scholar
  21. [21]
    Germain, E.,KK-theory of reduced free-productC *-algebras.Duke Math. J., 82 (1996), 707–723.CrossRefMATHMathSciNetGoogle Scholar
  22. [22]
    —,KK-theory of the full free product of unitalC *-algebras.J. Reine Angew. Math., 485 (1997), 1–10.MATHMathSciNetGoogle Scholar
  23. [23]
    —,K-theory of the commutator ideal.K-Theory, 23 (2001), 41–52.CrossRefMATHMathSciNetGoogle Scholar
  24. [24]
    Germain, E., A note on Toeplitz-Pimsner algebras and theK-theory of some of their subalgebras. Preprint.Google Scholar
  25. [25]
    Kirchberg, E., Commutants of unitaries in UHF algebras and functorial properties of exactness.J. Reine Angew. Math., 452 (1994), 39–77.MATHMathSciNetGoogle Scholar
  26. [26]
    Kirchberg, E., The classification of purely infiniteC *-algebras using Kasparov's theory. Preprint.Google Scholar
  27. [27]
    Kirchberg, E. &Phillips, N. C., Embedding of exactC *-algebras in the Cuntz algebraO 2.J. Reine Angew. Math., 525 (2000), 17–53.MathSciNetMATHGoogle Scholar
  28. [28]
    Kirchberg, E. &Rørdam, M., Non-simple purely infiniteC *-algebras.Amer. J. Math., 122 (2000), 637–666.MathSciNetMATHGoogle Scholar
  29. [29]
    Narnhofer, H., Størmer, E. &Thirring, W.,C *-dynamical systems for which the tensor product formula for entropy fails.Ergodic Theory Dynam. Systems, 15 (1995), 961–968.MathSciNetMATHGoogle Scholar
  30. [30]
    Neshveyev, S. &Størmer, E., The variational principle for a class of asymtotically abelianC *-algebras.Comm. Math. Phys., 215 (2000), 177–196.CrossRefMathSciNetMATHGoogle Scholar
  31. [31]
    Paulsen, V.,Completely Bounded Maps and Dilations. Pitman Res. Notes Math. Ser., 146. Longman, New York, 1986.MATHGoogle Scholar
  32. [32]
    Phillips, N. C., A classification theorem for nuclear purely infinite simpleC *-algebras.Doc. Math., 5 (2000), 49–114 (electronic).MATHMathSciNetGoogle Scholar
  33. [33]
    Pimsner, M., A class ofC *-algebras generalizing both Cuntz-Krieger algebras and crossed products byZ, inFree Probability Theory (Waterloo, ON, 1995) pp. 189–212. Fields Inst. Commun., 12. Amer. Math. Soc., Providence, RI, 1997.Google Scholar
  34. [34]
    Pinzari, C., Watatani, Y. &Yonetani, K., KMS states, entropy and the variational principle in fullC *-dynamical systems.Comm. Math. Phys., 213 (2000), 331–379.CrossRefMathSciNetMATHGoogle Scholar
  35. [35]
    Shlyakhtenko, D., Some applications of freeness with amalgamation.J. Reine Angew. Math., 500 (1998), 191–212.MATHMathSciNetGoogle Scholar
  36. [36]
    —, Free entropy with respect to a completely positive map.Amer. J. Math., 122 (2000), 45–81.MATHMathSciNetGoogle Scholar
  37. [37]
    Speicher, R.,Combinatorial Theory of the Free Product with Amalgamation and Operator-Valued Free Probability Theory. Mem. Amer. Math. Soc., 132. Amer. Math. Soc., Providence, RI, 1998.Google Scholar
  38. [38]
    Størmer, E., Entropy of some automorphisms of the II1-factor of the free group in infinite number of generators.Invent. Math., 110 (1992), 63–73.CrossRefMATHMathSciNetGoogle Scholar
  39. [39]
    —, States and shifts on infinite free products ofC *-algebras, inFree Probability Theory (Waterloo, ON, 1995), pp. 281–291. Fields Inst. Commun., 12. Amer. Math. Soc., Providence, RI, 1997.Google Scholar
  40. [40]
    —, A survey of noncommutative dynamical entropy, inClassification of Nuclear C *-algebras. Entropy in Operator Algebras, pp. 147–198. Encyclopaedia Math. Sci., 126. Springer-Verlag, Berlin, 2002.Google Scholar
  41. [41]
    Størmer, E. &Voiculescu, D., Entropy of Bogolyubov automorphisms of the canonical anticommutation relations.Comm. Math. Phys., 133 (1990), 521–542.CrossRefMathSciNetGoogle Scholar
  42. [42]
    Voiculescu, D., Symmetries of some reduced free productC *-algebras, inOperator Algebras and Their Connections with Topology and Ergodic Theory (Buşteni, 1983), pp. 556–588. Lecture Notes in Math., 1132. Springer-Verlag, 1985.Google Scholar
  43. [43]
    —, On the existence of quasicentral approximate units relative to normed ideals, I.J. Funct. Anal., 91 (1990), 1–36.CrossRefMATHMathSciNetGoogle Scholar
  44. [44]
    —, Dynamical approximation entropies and topological entropy in operator algebras.Comm. Math. Phys., 170 (1995), 249–281.CrossRefMATHMathSciNetGoogle Scholar
  45. [45]
    Voiculescu, D. V., Dykema, K. &Nica, A.,Free Random Variables. A Noncommutative Probability Approach to Free Products with Applications to Random Matrices, Operator Algebras and Harmonic Analysis on Free Groups. CRM Monograph Series, 1. Amer. Math. Soc., Providence, RI, 1992.MATHGoogle Scholar

Copyright information

© Institut Mittag-Leffler 2002

Authors and Affiliations

  • N. P. Brown
    • 1
  • K. Dykema
    • 2
  • D. Shlyakhtenko
    • 3
  1. 1.Department of MathematicsPennsylvania State UniversityState CollegeUSA
  2. 2.Department of MathematicsTexas A & M UniversityCollege StationUSA
  3. 3.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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