Mathematische Annalen

, Volume 283, Issue 4, pp 631–643

Continuous fields ofC*-algebras coming from group cocycles and actions

  • Marc A. Rieffel
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References

  1. 1.
    Anantharaman-Delaroche, C.: Systèm dynamiques non commutatifs et moyenabilité. Math. Ann.279, 297–315 (1987)Google Scholar
  2. 2.
    Anderson, J., Paschke, W.: The rotation algebra. MSRI preprintGoogle Scholar
  3. 3.
    Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., Sternheimer, D.: Deformation theory and quantization. I. II. Ann. Phys.110, 61–110; 111–151 (1978)Google Scholar
  4. 4.
    Bellissard, J.: K-theory ofC *-algebras in solid state physics Statistical mechanics and field theory, mathematical aspects, (Lect. Notes Phys., Vol. 257, 99–156). Berlin Heidelberg New York: Springer 1986Google Scholar
  5. 5.
    Belissard, J.: Ordinary quantum Hall effect and non-commutative cohomology. Proceedings Bad Schandau Conference on Localization, Leipzig: Teubner (to appear)Google Scholar
  6. 6.
    Belissard, J.:C *-algebras in solid state physics, 2D electrons in a uniform magnetic field. PreprintGoogle Scholar
  7. 7.
    Busby, R.C.: On the equivalence of twisted group algebras and Banach*-algebraic bundles. Proceedings A.M.S.37, 142–148 (1973)Google Scholar
  8. 8.
    Busby, R.C., Smith, H.A.: Representations of twisted group algebras. Trans. A.M.S.149, 503–537 (1970)Google Scholar
  9. 9.
    Dupré, M.J., Gillette, R.M.: Banach bundles, Banach modules and automorphisms ofC *-algebras. Research Notes in Math.92. London: Pitman 1983Google Scholar
  10. 10.
    Effros, E.G., Haagerup, U.: Lifting problems and local reflexivity forC *-algebras. Duke Math. J.52, 103–128 (1985)Google Scholar
  11. 11.
    Elliott, G.A.: Gaps in the spectrum of an almost periodic Schrödinger operator. C.R. Math. Rep. Acad. Sci. Canada4, 255–259 (1982)Google Scholar
  12. 12.
    Elliott, G.A.: On theK-theory of theC *-algebra generated by a projective representations of a torsion-free discrete abelian group. Operator algebras and group representations, vol. 1, pp. 157–184, London: Pitman 1984Google Scholar
  13. 13.
    Elliott, G.A.: Gaps in the spectrum of a almost periodic Schrödinger operator. II. Geometric methods in operator algebras, Araki, H., Effros, E.G. (eds.), pp. 181–191. London: Longman 1986Google Scholar
  14. 14.
    Fell, J.M.G.: An extension of Mackey's method to Banach*-algebraic bundles. Mem. A.M.S.90 (1969)Google Scholar
  15. 15.
    Fell, J.M.G.: Induced representations and Banach*-algebraic bundles, (Lecture Notes Math.582) Berlin Heidelberg New York: Springer 1977Google Scholar
  16. 16.
    Kehlet, E.T.: Cross sections for quotient maps of locally compact groups. Math. Scand.55, 152–160 (1984)Google Scholar
  17. 17.
    Kirchberg, E.: The Fubini theorem for exactC *-algebras. J. Oper. Theory10, 3–8 (1983)Google Scholar
  18. 18.
    Lee, R.-Y.: On theC *-algebras of operator fields. Indiana U. Math. J.25, 303–314 (1976)Google Scholar
  19. 19.
    Lichnerowicz A.: Deformations and quantization. Geometry and physics. Modugno, E., ed., pp. 103–116. Bologna: Pitagory 1983Google Scholar
  20. 20.
    Leinert, M.: Fell-Bündel und verallgemeinerteL 1-Algebren. J. Funct. Anal.22, 323–345 (1976)Google Scholar
  21. 21.
    Leptin, H.: VerallgemeinerteL 1-Algebren. Math. Ann.159, 51–76 (1965)Google Scholar
  22. 22.
    Leptin, H.: VerallgemeinerteL 1-Algebren und projektive Darstellungen lokal kompakter Gruppen. Invent. Math.3, 257–281 (1967)Google Scholar
  23. 23.
    Leptin, H.: Darstellungen verallgemeinerterL 1-Algebren. II. Lecture Note Math. 247, 251–307. Berlin Heidelberg New York: Springer 1972Google Scholar
  24. 24.
    Packer, J.A., Raeburn, I.: Twisted crossed products ofC *-algebras. PreprintGoogle Scholar
  25. 25.
    Pedersen, G.K.:C *-algebras and their automorphism groups. Lond. Math. Soc. Monographs 14. London: Academic Press 1979Google Scholar
  26. 26.
    Rieffel, M.A.: Proper actions of groups onC *-algebras. PreprintGoogle Scholar
  27. 27.
    Rieffel, M.A.: Deformation quantization for Heisenberg manifolds. PreprintGoogle Scholar
  28. 28.
    Smith, H.A.: Central twisted group algebras. Trans. A.M.S.238, 309–320 (1978)Google Scholar
  29. 29.
    William, D.P.: The structure of crossed products by smooth actions. J. Aust. Math. Soc. Ser. A (to appear)Google Scholar
  30. 30.
    Xia, J.: Geometric invariants of the quantum Hall effect. PreprintGoogle Scholar
  31. 31.
    Zeller-Meier, G.: Produits croisés d'uneC *-algèbre par un group d'automorphisms. J. Math. Pures Appl.47, 101–239 (1968)Google Scholar
  32. 32.
    Renault, J.: A groupoid approach toC *-algebras. (Lecture Notes Math.. 793). Berlin heidelberg New York: Springer 1980Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Marc A. Rieffel
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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