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Endomorphisms of type II1-factors and Cuntz algebras

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  09 April 2009

Masatoshi Enomoto  and
Yasuo Watatani
Masatoshi Enomoto
Affiliation:
College of Business and Administration ScienceKoshien UniversityTakarazuka, Hyogo, 665, Japan
Yasuo Watatani
Affiliation:
Department of MathematicsKyushu UniversityRopponmatsu, Fukuoka, 810, Japan
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Abstract

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Any unital *-endomorphism of a type II1-factor is implemented by isometries of a Cuntz algebra outside the factor. If the Jones index of the range of the *-endomorphism is an integer and the algebras act on the standard space, the Jones index must agree with the number of the generators of the Cuntz algebra. We also study (outer) conjugacy of *-endomorphisms using Cuntz algebras.

MSC classification

Secondary: 46L10: General theory of von Neumann algebras 46L35: Classifications of $C^*$-algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 60 , Issue 3 , June 1996 , pp. 343 - 354
Copyright
Copyright © Australian Mathematical Society 1996

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