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EXTENSION ALGEBRAS OF CUNTZ ALGEBRA, II

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  08 June 2009

SHUDONG LIU  and
XIAOCHUN FANG
SHUDONG LIU*
Affiliation:
School of Mathematical Sciences, Qufu Normal University, Qufu, People’s Republic of China (email: lshd008@163.com)
XIAOCHUN FANG
Affiliation:
Department of Mathematics, Tongji University, Shanghai, People’s Republic of China (email: xfang@mail.tongji.edu.cn)
*
✉For correspondence; e-mail: lshd008@163.com
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Abstract

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In this paper, we construct the unique (up to isomorphism) extension algebra, denoted by E∞, of the Cuntz algebra 𝒪∞ by the C*-algebra of compact operators on a separable infinite-dimensional Hilbert space. We prove that two unital monomorphisms from E∞ to a unital purely infinite simple C*-algebra are approximately unitarily equivalent if and only if they induce the same homomorphisms in K-theory.

Keywords

C*-algebraextensionCuntz algebra

MSC classification

Secondary: 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 1 , August 2009 , pp. 83 - 90
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

This work was supported by the National Natural Science Foundation of China (grant no. 10771161) and the Natural Science Foundation of Shandong Province (grant no. Y2006A03).

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