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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Crossed products of Hilbert $\mathrm{C}^{\ast}$-bimodules
by countable discrete groups


Authors: Tsuyoshi Kajiwara and Yasuo Watatani
Journal: Proc. Amer. Math. Soc. 126 (1998), 841-851
MSC (1991): Primary 46L05, 46L37, 46L55
MathSciNet review: 1423344
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Abstract: We introduce a notion of crossed products of Hilbert C${}^{*}$-bimodules by countable discrete groups and mainly study the case of finite groups following Jones index theory. We give a sufficient condition such that the crossed product bimodule is irreducible. We have a bimodule version of Takesaki-Takai duality. We show the categorical structures when the action is properly outer, and give some example of this construction concerning the orbifold constructions.


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Additional Information

Tsuyoshi Kajiwara
Affiliation: Department of Environmental and Mathematical Sciences, Okayama University, Tsushima, Okayama 700, Japan
Email: kajiwara@math.ems.okayama-4.ac.jp

Yasuo Watatani
Affiliation: Graduate School of Mathematics, Kyushu University, Ropponmatsu, Fukuoka, 810 Japan
Email: watatani@rc.kyush-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04118-5
PII: S 0002-9939(98)04118-5
Received by editor(s): May 15, 1996
Received by editor(s) in revised form: September 10, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society