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Crossed products of Hilbert C*-bimodules by bundles

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  09 April 2009

Tsuyoshi Kajiwara  and
Yasuo Watatani
Tsuyoshi Kajiwara
Affiliation:
Department of Environmental and Mathematical Sciences Okayama UniversityTsushima, 700, Japan
Yasuo Watatani
Affiliation:
Graduate School of Mathematics Kyushu UniversityRopponmatsu Fukuoka, 810, Japan
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Abstract

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We present the definition of crossed products of Hilbert C*-bimodules by Hilbert bundles with commuting finite group actions and finite dimensional fibers. This is a general construction containing the bundle construction and crossed products of Hilbert C*-bimodule by finite groups. We also study the structure of endomorphism algebras of the tensor products of bimodules. We also define the multiple crossed products using three bimodules containing more than 2 bundles and show the associativity law. Moreover, we present some examples of crossed product bimodules easily computed by our method.

MSC classification

Secondary: 46L35: Classifications of $C^*$-algebras 46L55: Noncommutative dynamical systems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 64 , Issue 1 , February 1998 , pp. 119 - 135
Copyright
Copyright © Australian Mathematical Society 1998

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