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

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References

  1. Anantharaman-Delaroche, C.: Systèm dynamiques non commutatifs et moyenabilité. Math. Ann.279, 297–315 (1987)

    Google Scholar 

  2. Anderson, J., Paschke, W.: The rotation algebra. MSRI preprint

  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. 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 1986

    Google Scholar 

  5. Belissard, J.: Ordinary quantum Hall effect and non-commutative cohomology. Proceedings Bad Schandau Conference on Localization, Leipzig: Teubner (to appear)

  6. Belissard, J.:C *-algebras in solid state physics, 2D electrons in a uniform magnetic field. Preprint

  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. Busby, R.C., Smith, H.A.: Representations of twisted group algebras. Trans. A.M.S.149, 503–537 (1970)

    Google Scholar 

  9. Dupré, M.J., Gillette, R.M.: Banach bundles, Banach modules and automorphisms ofC *-algebras. Research Notes in Math.92. London: Pitman 1983

    Google Scholar 

  10. Effros, E.G., Haagerup, U.: Lifting problems and local reflexivity forC *-algebras. Duke Math. J.52, 103–128 (1985)

    Google Scholar 

  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. 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 1984

    Google Scholar 

  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 1986

    Google Scholar 

  14. Fell, J.M.G.: An extension of Mackey's method to Banach*-algebraic bundles. Mem. A.M.S.90 (1969)

  15. Fell, J.M.G.: Induced representations and Banach*-algebraic bundles, (Lecture Notes Math.582) Berlin Heidelberg New York: Springer 1977

    Google Scholar 

  16. Kehlet, E.T.: Cross sections for quotient maps of locally compact groups. Math. Scand.55, 152–160 (1984)

    Google Scholar 

  17. Kirchberg, E.: The Fubini theorem for exactC *-algebras. J. Oper. Theory10, 3–8 (1983)

    Google Scholar 

  18. Lee, R.-Y.: On theC *-algebras of operator fields. Indiana U. Math. J.25, 303–314 (1976)

    Google Scholar 

  19. Lichnerowicz A.: Deformations and quantization. Geometry and physics. Modugno, E., ed., pp. 103–116. Bologna: Pitagory 1983

    Google Scholar 

  20. Leinert, M.: Fell-Bündel und verallgemeinerteL 1-Algebren. J. Funct. Anal.22, 323–345 (1976)

    Google Scholar 

  21. Leptin, H.: VerallgemeinerteL 1-Algebren. Math. Ann.159, 51–76 (1965)

    Google Scholar 

  22. Leptin, H.: VerallgemeinerteL 1-Algebren und projektive Darstellungen lokal kompakter Gruppen. Invent. Math.3, 257–281 (1967)

    Google Scholar 

  23. Leptin, H.: Darstellungen verallgemeinerterL 1-Algebren. II. Lecture Note Math. 247, 251–307. Berlin Heidelberg New York: Springer 1972

    Google Scholar 

  24. Packer, J.A., Raeburn, I.: Twisted crossed products ofC *-algebras. Preprint

  25. Pedersen, G.K.:C *-algebras and their automorphism groups. Lond. Math. Soc. Monographs 14. London: Academic Press 1979

    Google Scholar 

  26. Rieffel, M.A.: Proper actions of groups onC *-algebras. Preprint

  27. Rieffel, M.A.: Deformation quantization for Heisenberg manifolds. Preprint

  28. Smith, H.A.: Central twisted group algebras. Trans. A.M.S.238, 309–320 (1978)

    Google Scholar 

  29. William, D.P.: The structure of crossed products by smooth actions. J. Aust. Math. Soc. Ser. A (to appear)

  30. Xia, J.: Geometric invariants of the quantum Hall effect. Preprint

  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. Renault, J.: A groupoid approach toC *-algebras. (Lecture Notes Math.. 793). Berlin heidelberg New York: Springer 1980

    Google Scholar 

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Supported in part by National Science Foundation grant DMS 8601900

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Rieffel, M.A. Continuous fields ofC *-algebras coming from group cocycles and actions. Math. Ann. 283, 631–643 (1989). https://doi.org/10.1007/BF01442857

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