Crossed products with continuous trace

Memoirs of the American Mathematical Society

Volumn , Issue 586, 1996, Pages 1-134

  Echterhoff, Siegfried ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030243683     PISSN: 00659266     EISSN: None     Source Type: Journal    
DOI: 10.1090/memo/0586     Document Type: Article

References (71)

1. 1. L. Auslander and C. C. Moore. Unitary representations of solvable Lie groups. Memoirs Amer. Math. Soc., 62 (1966).
2. 2. L. W. Baggett, A. L. Carey, W. Moran, and A. Ramsay. Non-monomial multiplier representations of abelian groups. J. Funct. Anal., 97 (1991), 361-372.
3. 3. L. W. Baggett and A. Kleppner. Multiplier representations of abelian groups. J. Funct. Anal., 14 (1973), 299-324.
4. 4 L. G. Brown, P. Green, and M. A. Rieffel. Stable isomorphism and strong Morita equivalence of C*-algebras. Pacific J. Math., 71 (1977), 349-363.
5. 5. A. L. Carey and W. Moran. Non-monomial unitary representations of nilpotent groups I: The abelian case. Proc. London Math. Soc. (3), 46 (1983), 53-82.
6. 6. F. Combes. Crossed products and Morita equivalence. Proc. London Math. Soc. (3), 49 (1984), 289-306.
7. 7. J. Dixmier. Traces sur les C*-algèbres. Ann. Inst. Fourier, 13 (1963), 219-262.
8. 8. _,Sur le dual d'un groupe de Lie nilpotent. Bull. Sci. Math, 90 (1966), 113-118.
9. 9. _,C*-algebras. North-Holland, New York, 1977.
10. 10. S. Echterhoff. On induced covariant systems. Proc. Amer. Math. Soc., 108 (1990), 703-706.
11. 11. _,On maximal prime ideals in certain group C*-algebras and crossed product algebras. J. Operator Theory, 23 (1990), 317-318.
12. 12. _,The primitive ideal space of twisted covariant systems with continuously varying stabilizers. Math. Ann., 292 (1992), 59-84.
13. 13. _,Regularizations of twisted covariant systems and crossed products with continuous trace. J. Funct. Anal., 116 (1993), 277-314.
14. 14. _,On transformation group C*-algebras with continuous trace. Trans. Amer. Math. Soc., 343 (1994), 117-133.
15. 15. _,Morita equivalent actions and a new version of the Parker-Raeburn stabilization trick. J. London Math. Soc. (2), 50 (1994), 170-186.
16. 16. _,Duality of induction and restriction for abelian twisted covariant systems. Math. Proc. Camb. Phil. Soc., 116 (1994), 301-315.
17. 17. S. Echterhoff and E. Kaniuth. Certain group extensions and twisted covariance algebras with generalized continuous trace. In: Harmonic Analysis (Proceedings, 1987), Lecture Notes in Math., vol. 1359, pages 159-169, Springer-Verlag, Berlin, Heidelberg, New York, 1988.
18. 18. S. Echterhoff and I. Raeburn. The stabilization trick for coactions. preprint.
19. 19. S. Echterhoff and J. Rosenberg. Fine structure of the Mackey machine for actions of abelian groups with constant Mackey obstruction. Pacific J. Math. (to appear).
20. 20. S. Echterhoff and D. P. Williams. Crossed products whose primitive ideal spaces are generalized trivial Ĝ-bundles. Math. Ann. (to appear).
21. 21. J. M. G. Fell. A Hausdorff topology on the closed subsets of a locally compact non-Hausdorff space. Proc. Amer. Math. Soc., 13 (1962), 472-476.
22. 22. _,Weak containment and induced representations of groups. Canad. J. Math., 14 (1962), 237-268.
23. 23. _,Weak containment and Kronecker products of group representations. Pacific J. Math., 13 (1963), 503-510.
24. 24. _,Weak containment and induced representations of groups, II. Trans. Amer. Math. Soc., 110 (1964), 424-447.
25. 25. _,An extension of Mackey's method to Banach *-algebraic bundles. Memoirs Amer. Math. Soc., 90 (1969).
26. 26. A. Gleason. Spaces with a compact Lie group of tranformations. Proc. Amer. Math. Soc., 1 (1950), 35-43.
27. 27. J. Glimm. Families of induced representations. Pacific J. Math., 72 (1962), 885-911.
28. 28. E. C. Gootman. Abelian group actions on type I C*-algebras. In: Operator Algebras and their Connections with Topology and Ergodic Theory, vol. 1132 of Lecture Notes in Mathematics, pp. 152-169, Buşteni, Romania, 1983. Springler-Verlag.
29. 29. E. C. Gootman and A. Lazar. Crossed products of type I AF algebras by abelian groups. Israel J. Math., 56 (1986), 267-279.
30. 30. E. C. Gootman and D. Olesen. Spectra of actions on type I C*-algebras. Math.-Scand., 47 (1980), 329-349.
31. 31. E. C. Gootman and J. Rosenberg. The structure of crossed products C*-algebras: A proof of the generalized Effros-Hahn conjecture. Invent. Math., 52 (1979), 283-298.
32. 32. P. Green. C*-algebras of transformation groups with smooth orbit space. Pacific J. Math., 72 (1977), 71-97.
33. 33. _,The local structure of twisted covariance algebras. Acta. Math., 140 (1978), 191-250.
34. 34. K. C. Hannabuss. Representations of nilpotent locally compact groups. J. Funct. Anal., 34 (1974), 146-165.
35. 35. S. Hurder, D. Olesen, I. Raeburn, and J. Rosenberg. The Connes spectrum for actions of abelian groups on continuous-trace algebras. Ergod. Th. & Dynam. Sys., 6 (1986), 541-560.
36. 36. R.-Y. Lee. On the C*-algebras of operator fields. Indiana Univ. Math. J., 25 (1976), 303-314.
37. 37. R. L. Lipsman and J. Rosenberg. The behavior of Fourier transforms for nilpotent Lie groups. preprint.
38. 38. G. W. Mackey. Imprimitivity for representations of locally compact groups, I. Proc. Nat. Acad. Sci. U. S. A., 35 (1949), 537-545.
39. 39. _,On induced representations of groups. Amer. J. Math., 73 (1951), 576-592.
40. 40. _,Induced representations of locally compact groups. I. Ann. Math., 55 (1952), 101-139.
41. 41. _,Unitary representations of group extensions. I. Acta math., 99 (1958), 265-311.
42. 42. C. C. Moore. Group extensions and cohomology for locally compact groups. III. Trans. Amer. Math. Soc., 221 (1976), 1-33.
43. 43. _,Group extensions and cohomology for locally compact groups. IV. Trans. Amer. Math. Soc., 221 (1976), 34-58.
44. 44. P. S. Muhly and D. P. Williams. Transformation group C*-algebras with continuous trace. II. J. Operator Theory, 11 (1984), 109-124.
45. 45. O. A. Nielsen. Unitary representations and coadjoint orbits of low-dimensional nilpotent Lie groups. Queen's Papers in Pure and Applied Mathematics No 63, Kingston 1983.
46. 46. D. Olesen and I. Raeburn. Pointwise unitary automorphism groups. J. Funct. Anal., 93 (1990), 278-309.
47. 47. J. A. Packer and I. Raeburn. Twisted crossed products of C*-algebras. Math. Proc. Camb. Phil. Soc., 106 (1989), 293-311.
48. 48. R. S. Palais. On the existence of slices for actions of non-compact Lie groups. Ann. Math., 73 (1961), 295-323.
49. 49. G. K. Pedersen. A decomposition theorem for C*-algebras. Math.-Scand., 22 (1968), 266-268.
50. 50. _,C*-Algebras and their Automorphism Groups. Academic Press, London, 1979.
51. 51. N. V. Pedersen. On the infinitesimal kernel of irreducible representations of nilpotent Lie groups. Bull. Soc. math. France, 112 (1984), 423-467.
52. 52. J. Phillips and I. Raeburn. Crossed products by locally unitary automorphism groups and principal bundles. J. Operator Theory, 11 (1984), 215-241.
53. 53. I. Raeburn. On crossed products by coactions and their representation theory. Proc. London Math. Soc., 64 (1992), 625-652.
54. 54. I. Raeburn and J. Rosenberg. Crossed products of continuous-trace C*-algebras by smooth actions. Trans. Amer. Math. Soc., 305 (1988), 1-45.
55. 55. I. Raeburn and D. P. Williams. Pull-backs of C*-algebras and crossed products by certain diagonal actions. Trans. Amer. Math. Soc., 287 (1985) 755-777.
56. 56. _,Crossed products by actions which are locally unitary on the stabilisers. J. Funct. Anal., 81 (1988), 385-431.
57. 57. _,Moore cohomology, principal bundles, and actions of groups on C*-algebras. Indiana U. Math. J., 40 (1991), 707-740.
58. 58. _,Topological invariants associated to the spectrum of crossed product C*-algebras. J. Funct. Anal., 116 (1993), 245-276.
59. 59. _,Dixmier-Douady classes for dynamical systems and crossed products. Canad. J. Math., 45(5), (1993), 1032-1066.
60. 60. _,Equivariant cohomology and a Gysin sequence for principal bundles. preprint.
61. 61. J. Renault. Reprśentations des produits croisés d'algèbres de groupoides. J. Operator Theory., 18 (1987), 361-363.
62. 62. M. A. Rieffel. Induced representations of C*-algebras. Adv. in Math., 13 (1974), 176-257.
63. 63. _,Unitary representations of group extensions: an algebraic approach to the theory of Mackey and Blattner. Adv. in Math. Supplementary Studies, 4 (1979), 43-81.
64. 64. J. Rosenberg. Some results on cohomology with Borel cochains, with applications to group actions on operator algebras. Operator Theory: Advances and Applications, 17 (1986), 301-330.
65. 65. _,C*-algebras and Mackey's theory of group representations. In: C*-algebras: 1943-1993, a Fifty-Year Celebration (R. S. Doran, ed.), Contemp. Math., vol. 167, Amer. Math. Soc., Providence, RI, 1994.
66. 66. _,Continuous-trace algebras from the bundle-theoretic point of view. J. Aust. Math. Soc. (Series A), 47 (1989), 368-381.
67. 67. J.-L. Sauvageot. Ideaux primitifs de certain produits croises. Math. Ann., 231 (1977), 61-76.
68. 68. I. Schochetman. the dual topology of certain group extensions. Adv. in Math., 35 (1980), 113-128.
69. 69. M. Takesaki. Covariant representations of C*-algebras and their locally compact automorphism groups. Acta Math., 119 (1967), 273-303.
70. 70. D. P. Williams. Transformation group C*-algebras with continuous trace. J. Funct. Anal., 41 (1981), 40-76.
71. 71. _,Transformation group C*-algebras with Hausdorff sprectrum. Illinois J. Math., 26 (1982), 317-321.