Skip to main content
SpringerLink
Log in

The local structure of twisted covariance algebras

  • Published:
Acta Mathematica

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Akemann, C. A., Pedersen, G. K. &Tomiyama, J., Multipliers of C*-algebras.J. Functional Analysis, 13 (1973), 277–301.

    Article  MathSciNet  Google Scholar 

  2. Auslander, L. & Moore, C. C., Unitary representations of solvable Lie groups.Mem. Amer. Math. Soc., no. 62 (1966).

  3. Baggett, L. &Kleppner, A., Multiplier representations of abelian groups.J. Functional Analysis, 14 (1973), 299–324.

    Article  MathSciNet  Google Scholar 

  4. Blackadar, B., Infinite tensor products of C*-algebras.Pacific J. Math., 72 (1977), 313–334.

    MATH  MathSciNet  Google Scholar 

  5. Blattner, R. J., Group extension representations and the structure space.Pacific J. Math., 15 (1965), 1101–1113.

    MATH  MathSciNet  Google Scholar 

  6. Bunce, J. W. &Deddens, J. A., A family of simple C*-algebras related to weighted shift operators.J. Functional Analysis, 19 (1975), 13–24.

    Article  MathSciNet  Google Scholar 

  7. Busby, R. C., Double centralizers and extensions of C*-algebras.Trans. Amer. Math. Soc., 132 (1968), 79–99.

    Article  MATH  MathSciNet  Google Scholar 

  8. Busby, R. C. &Smith, H. A., Representations of twisted group algebras.Trans. Amer. Math. Soc., 147 (1970), 503–537.

    Article  MathSciNet  Google Scholar 

  9. Chevalley, C.,Theorie des groupes de Lie, vol. 2, Groupes algébriques. Acta. Sci. Ind., no. 1152, Hermann, Paris, 1951.

    Google Scholar 

  10. Choi, M. D. &Effros, E. G., Nuclear C*-algebras and injectivity: the genral case.Indiana Univ. Math. J., 26 (1977), 443–446.

    Article  MathSciNet  Google Scholar 

  11. Connes, A., Classification of injective factors.Annals of Math., 104 (1976), 73–115.

    Article  MATH  MathSciNet  Google Scholar 

  12. Dang Ngoc, N., Produits croisés restreints, et extensions de groupes, preprint.

  13. Dixmier, J., Ideal center of a C*-algebra.Duke Math. J., 35 (1968), 375–382.

    Article  MATH  MathSciNet  Google Scholar 

  14. —, Sur la représentation régulière d’un groupe localement compact connexe.Ann. Sci. École Norm. Sup., 2 (1969), 423–436.

    MATH  MathSciNet  Google Scholar 

  15. —,Les C *-algèbres et leurs représentations, 2e ed. Gauthier-Villars, Paris, 1969.

    Google Scholar 

  16. —,Les algèbres d’opérateurs dans l’espace Hilbertien, 2e ed. Gauthier-Villars, Paris, 1969.

    Google Scholar 

  17. —, Bicontinuité dans la méthode du petit groupe de Mackey.Bull. Sci. Math., 97 (1973), 233–240.

    MathSciNet  Google Scholar 

  18. Doplicher, S., Kastler, D. &Robinson, D. W., Covariance algebras in field theory and statistical mechanics.Comm. Math. Phys., 3 (1966), 1–28.

    Article  MathSciNet  Google Scholar 

  19. Effros, E. G., A decomposition theory for representations of C*-algebras.Trans. Amer. Math. Soc., 107 (1963), 83–106.

    Article  MATH  MathSciNet  Google Scholar 

  20. Effros, E. G. & Hahn, F. Locally compact transformation groups and C*-algebras.Mem. Amer. Math. Soc., no. 75 (1967).

  21. Eymard, P.,Moyennes invariantes et représentations unitaires. Lecture Notes in Math. no. 300, Springer, Berlin, 1972.

    Google Scholar 

  22. Fell, J. M. G., Weak containment and induced representations of groups.Canad. J. Math., 14 (1962), 237–268.

    MATH  MathSciNet  Google Scholar 

  23. —, Weak containment and induced representations of groups, II.Trans Amer. Math. Soc., 110 (1964), 424–447.

    Article  MATH  MathSciNet  Google Scholar 

  24. Fell, J. M. G., An extension of Mackey’s method to Banach*-algebraic bundles.Mem. Amer. Math. Soc., no. 90 (1969).

  25. Glimm, J., Locally compact transformation groups.Trans. Amer. Math. Soc., 101 (1961), 124–138.

    Article  MATH  MathSciNet  Google Scholar 

  26. Glimm, J., Families of induced representations.Pacific J. Math., 12 (1962), 885–911.

    MATH  MathSciNet  Google Scholar 

  27. Gootman, E. C., Primitive ideals of C*-algebras associated with transformation groups.Trans. Amer. Math. Soc., 170 (1972), 97–108.

    Article  MATH  MathSciNet  Google Scholar 

  28. —, Local eigenvectors for group representations.Studia Math., 53 (1975), 135–138.

    MATH  MathSciNet  Google Scholar 

  29. Green, P., C*-algebras of transformation groups with smooth orbit space.Pacific J. Math., 72 (1977), 71–97.

    MATH  MathSciNet  Google Scholar 

  30. Green, P., Morita equivalence of C*-algebras. In preparation.

  31. Greenleaf, F. P.,Invariant means on topological groups and their applications, Van Nostrand, New York, 1969.

    Google Scholar 

  32. —, Amenable actions of locally compact groupsJ. Functional Analysis, 4 (1969), 295–315.

    Article  MATH  MathSciNet  Google Scholar 

  33. Guichardet, A., Caractères des algèbres de Banach involutives.Ann. Inst. Fourier, 13 (1962), 1–81.

    MathSciNet  Google Scholar 

  34. Guichardet, A., Tensor products of C*-algebras. Math. Inst. Aarhus Univ. Lecture Notes No. 12-13 (1969).

  35. Halpern, H., Quasi-equivalence classes of normal representations for a separable C*-algebra.Trans. Amer. Math. Soc., 203 (1975), 129–140.

    Article  MATH  MathSciNet  Google Scholar 

  36. Hewitt, E. &Ross, K. A.,Abstract harmonic analysis. Springer, Berlin, 1963.

    Google Scholar 

  37. Johnson, B. E., An introduction to the theory of centralizers.Proc. London Math. Soc., 14 (1964), 299–320.

    MATH  MathSciNet  Google Scholar 

  38. Kleppner, A., Non-type I multiplier representations of abelian groups. Preprint.

  39. Lance, C., On nuclear C*-algebras.J. Functional Analysis, 12 (1973), 157–176.

    Article  MATH  MathSciNet  Google Scholar 

  40. Leptin, H., Verallgemeinerte L1-Algebren.Math. Ann., 159 (1965), 51–76.

    Article  MATH  Google Scholar 

  41. —, Verallgemeinerte L1-Algebren und projective Darstellungen lokal kompakter Gruppen.Inventiones Math., 3 (1967), 257–281; 4, 68–86.

    Article  MATH  MathSciNet  Google Scholar 

  42. —, Darstellungen verallgemeinerter L1-Algebren.Inventiones Math., 5 (1968), 192–215.

    Article  MATH  MathSciNet  Google Scholar 

  43. Mackey, G. W., Imprimitivity for representations of locally compact groups, I,Proc. Nat. Acad. Sci. U.S.A., 35 (1949), 537–545.

    MATH  MathSciNet  Google Scholar 

  44. —, Unitary representations of group extensions I.Acta Math., 99 (1958), 265–311.

    MATH  MathSciNet  Google Scholar 

  45. Moore, C. C., Groups with finite dimensional irreducible representations.Trans. Amer. Math. Soc., 166 (1972), 401–410.

    Article  MATH  MathSciNet  Google Scholar 

  46. Moore, C. C. &Rosenberg, J., Groups with T1 primitive ideal spaces.J. Functional Analysis, 22 (1976), 204–224.

    Article  MathSciNet  Google Scholar 

  47. Pedersen, G. K., Measure theory for C*-algebras.Math. Scand., 19 (1966), 131–145.

    MathSciNet  Google Scholar 

  48. Pukanszky, L., Aetion of algebraic groups of automorphisms on the dual of a class of type I groups.Ann. Sci. École Norm Sup., 5 (1972), 379–396.

    MATH  MathSciNet  Google Scholar 

  49. —, Characters of connected Lie groups.Acta Math., 133 (1974), 81–137.

    MATH  MathSciNet  Google Scholar 

  50. Rieffel, M. A., Induced Banach representations of Banach algebras and locally compact groups.J. Functional Analysis, 1 (1967), 443–491.

    Article  MATH  MathSciNet  Google Scholar 

  51. —, Induced representations of C*-algebras.Advances in Math., 13 (1974), 176–257.

    Article  MATH  MathSciNet  Google Scholar 

  52. Rieffel, M. A., Unitary representations of group extensions: an algebraic approach to the theory of Mackey and Blattner. To appear inAdvances in Math.

  53. Sakai, S.,C *-algebras and W *-algebras. Springer, Berlin, 1971.

    Google Scholar 

  54. Takai, H., On a duality for crossed products of C*-algebras.J. Functional Analysis, 19 (1975), 25–39.

    Article  MATH  MathSciNet  Google Scholar 

  55. Takesaki, M., Covariant representations of C*-algebras and their locally compact automorphism groups.Acta Math., 119, (1967), 273–302.

    Article  MATH  MathSciNet  Google Scholar 

  56. —, A liminal crossed product of a uniformly hyperfinite algebra by a compact abelian automorphism groups.J. Functional Analysis, 7 (1971), 140–146.

    Article  MATH  MathSciNet  Google Scholar 

  57. Zeller-Meier, G., Produits croisés d’une C*-algebre par un groupe d’automorphismes.J. Math. Pures Appl., 47 (1968), 101–239.

    MATH  MathSciNet  Google Scholar 

  58. Rosenberg, J., Square-integrable factor representations of locally compact groups. To appear inTrans. Amer. Math. Soc.

  59. Brown, L., Green, P. &Rieffel, M., Stable isomorphism and strong Morita equivalence of C*-algebras.Pacific J. Math., 71 (1977), 349–363.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Columbia University, New York, N.Y., U.S.A.

    Philip Green

Authors
  1. Philip Green
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported in part by an NSF Graduate Fellowship and by a Grant-in-Aid from the Graduate Division of the University of California, Berkeley. This paper formed a portion of the author’s doctoral thesis, submitted to the Univ. of Calif. in September, 1976.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Green, P. The local structure of twisted covariance algebras. Acta Math. 140, 191–250 (1978). https://doi.org/10.1007/BF02392308

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02392308

Keywords

Search

Navigation