Crossed products of Hilbert -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

DOI:
https://doi.org/10.1090/S0002-9939-98-04118-5

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:
https://doi.org/10.1090/S0002-9939-98-04118-5

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