Morita equivalence of twisted crossed products

Bui, Huu Hung

doi:10.1090/S0002-9939-1995-1260162-1

Morita equivalence of twisted crossed products
HTML articles powered by AMS MathViewer

by Huu Hung Bui PDF

Proc. Amer. Math. Soc. 123 (1995), 2771-2776 Request permission

Abstract:

We introduce a natural notion of strong Morita equivalence of twisted actions of a locally compact group on ${C^ \ast }$-algebras, and then show that the corresponding twisted crossed products are strongly Morita equivalent. This result is a generalization of the result of Curto, Muhly and Williams concerning strong Morita equivalence of crossed products by actions.

References

Saad Baaj and Georges Skandalis, $C^\ast$-algèbres de Hopf et théorie de Kasparov équivariante, $K$-Theory 2 (1989), no. 6, 683–721 (French, with English summary). MR 1010978, DOI 10.1007/BF00538428
Nicolas Bourbaki, Espaces vectoriels topologiques. Chapitres 1 à 5, New edition, Masson, Paris, 1981 (French). Éléments de mathématique. [Elements of mathematics]. MR 633754
Huu Hung Bui, Morita equivalence of twisted crossed products by coactions, J. Funct. Anal. 123 (1994), no. 1, 59–98. MR 1279296, DOI 10.1006/jfan.1994.1083

Full coactions on Hilbert

modules

F. Combes, Crossed products and Morita equivalence, Proc. London Math. Soc. (3) 49 (1984), no. 2, 289–306. MR 748991, DOI 10.1112/plms/s3-49.2.289
Raúl E. Curto, Paul S. Muhly, and Dana P. Williams, Cross products of strongly Morita equivalent $C^{\ast }$-algebras, Proc. Amer. Math. Soc. 90 (1984), no. 4, 528–530. MR 733400, DOI 10.1090/S0002-9939-1984-0733400-1
N. Dinculeanu, Integration on locally compact spaces, Noordhoff International Publishing, Leiden, 1974. Translated from the Romanian. MR 0360981
Siegfried Echterhoff, Morita equivalent twisted actions and a new version of the Packer-Raeburn stabilization trick, J. London Math. Soc. (2) 50 (1994), no. 1, 170–186. MR 1277761, DOI 10.1112/jlms/50.1.170
Philip Green, The local structure of twisted covariance algebras, Acta Math. 140 (1978), no. 3-4, 191–250. MR 493349, DOI 10.1007/BF02392308
Judith A. Packer and Iain Raeburn, Twisted crossed products of $C^*$-algebras, Math. Proc. Cambridge Philos. Soc. 106 (1989), no. 2, 293–311. MR 1002543, DOI 10.1017/S0305004100078129
Iain Raeburn, Induced $C^*$-algebras and a symmetric imprimitivity theorem, Math. Ann. 280 (1988), no. 3, 369–387. MR 936317, DOI 10.1007/BF01456331
Marc A. Rieffel, Induced representations of $C^{\ast }$-algebras, Advances in Math. 13 (1974), 176–257. MR 353003, DOI 10.1016/0001-8708(74)90068-1
Marc A. Rieffel, $C^{\ast }$-algebras associated with irrational rotations, Pacific J. Math. 93 (1981), no. 2, 415–429. MR 623572, DOI 10.2140/pjm.1981.93.415

Applications of strong Morita equivalence to transformation group

algebras

Jonathan Rosenberg, Appendix to: “Crossed products of UHF algebras by product type actions” [Duke Math. J. 46 (1979), no. 1, 1–23; MR 82a:46063 above] by O. Bratteli, Duke Math. J. 46 (1979), no. 1, 25–26. MR 523599
Masamichi Takesaki, Theory of operator algebras. I, Springer-Verlag, New York-Heidelberg, 1979. MR 548728, DOI 10.1007/978-1-4612-6188-9