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A remark on Mansfield's imprimitivity theorem


Author: Chi-Keung Ng
Journal: Proc. Amer. Math. Soc. 126 (1998), 3767-3768
MSC (1991): Primary 46L55
DOI: https://doi.org/10.1090/S0002-9939-98-05066-7
MathSciNet review: 1626462
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Abstract: We show that the Morita equivalence part of Mansfield's Imprimitivity Theory can be obtained by Green's Imprimitivity Theorem (and duality theory).


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  • [1] S. Baaj and G. Skandalis, $C^{*}$-algèbres de Hopf et théorie de Kasparov équivariante, $K$-theory 2 (1989), 683-721. MR 90j:46061
  • [2] P. Green, The local structure of twisted covariance algebras, Acta. Math. 140 (1978), 191-250. MR 58:12376
  • [3] Y. Katayama, Takesaki's duality for a nondegenerate coaction, Math. Scand. 55 (1984), 141-151. MR 86b:46112
  • [4] M. B. Landstad, J. Phillips, I. Raeburn and C. E. Sutherland, Representations of crossed products by coactions and principal bundles, Trans.Amer. Math. Society, Vol 299 (1987), No. 2, 747-784. MR 88f:46127
  • [5] K. Mansfield, Induced representations of crossed products by coactions, J. Funct. Anal., 97 (1991), no. 1, 112-161. MR 92h:46095
  • [6] C. K. Ng, Coactions and crossed products of Hopf $C^{*}$-algebras, Proc. London Math. Soc. (3) 72 (1996), 638-656. MR 97d:46083
  • [7] J. Quigg, Full and reduced $C^*$-coactions, Math. Proc. Camb. Phil. Soc. 116 (1994), 425-450. MR 95g:46126
  • [8] I. Raeburn, On crossed products by coactions and their representation theory, Proc. London Math. Soc. (3), 64 (1992), 625-652. MR 93e:46080
  • [9] M. A. Rieffel, Induced representations of $C^{*}$-algebras, Adv. in Math. 13 (1974), 176-257. MR 50:5489
  • [10] M. A. Rieffel, Strong Morita equivalence of certain transformation group $C^*$-algebras, Math. Ann. 222 (1976), 7-22. MR 54:7695

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Additional Information

Chi-Keung Ng
Affiliation: Mathematical Institute, Oxford University, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom
Email: ng@maths.ox.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-98-05066-7
Keywords: Coactions, crossed products, Imprimitivity Theorem, Morita equivalence
Received by editor(s): June 20, 1997
Communicated by: David R. Larson
Article copyright: © Copyright 1998 American Mathematical Society

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