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A CHARACTERIZATION OF SATURATED C*-ALGEBRAIC BUNDLES OVER FINITE GROUPS

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  04 June 2010

KAZUNORI KODAKA  and
TAMOTSU TERUYA
KAZUNORI KODAKA*
Affiliation:
Department of Mathematical Sciences, Faculty of Science, Ryukyu University, Nishihara-cho, Okinawa 903-0213, Japan (email: kodaka@math.u-ryukyu.ac.jp)
TAMOTSU TERUYA
Affiliation:
Department of Mathematical Sciences, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan
*
✉For correspondence; e-mail: kodaka@math.u-ryukyu.ac.jp
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Abstract

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Let A be a unital C*-algebra. Let (B,E) be a pair consisting of a unital C*-algebra B containing A as a C*-subalgebra with a unit that is also the unit of B, and a conditional expectation E from B onto A that is of index-finite type and of depth 2. Let B1 be the C*-basic construction induced by (B,E). In this paper, we shall show that any such pair (B,E) satisfying the conditions that A′∩B=ℂ1 and that A′∩B1 is commutative is constructed by a saturated C*-algebraic bundle over a finite group. Furthermore, we shall give a necessary and sufficient condition for B to be described as a twisted crossed product of A by its twisted action of a finite group under the condition that A′∩B1 is commutative.

Keywords

conditional expectationsC*-algebraic bundlesdepth 2initial C*-algebrasWatatani indextwisted actionstwisted crossed products

MSC classification

Secondary: 46L08: $C^*$-modules
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 88 , Issue 3 , June 2010 , pp. 363 - 383
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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