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Purely Infinite Simple C*-Crossed Products II

Published online by Cambridge University Press:  20 November 2018

JA A. Jeong ,
Kazunori Kodaka  and
Hiroyuki Osaka
JA A. Jeong
Affiliation:
Global Analysis Research Center, Department of Mathematics, Seoul National University, Seoul 151-742, Korea
Kazunori Kodaka
Affiliation:
Department of Mathematics, College of Science, Ryukyu University, Nishihara-cho, Okinawa 903-01, Japan
Hiroyuki Osaka
Affiliation:
Department of Mathematics, College of Science, Ryukyu University, Nishihara-cho, Okinawa 903-01, Japan
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Abstract

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We study the pure infiniteness of C* -crossed products by endomorphisms and automorphisms. Let A be a purely infinité simple unital C*-algebra. At first we show that a crossed product A × p N by a corner endomorphism p is purely infinite if it is simple. From this observation we prove that any simple C*-crossed products A ×αZ by an automorphism α is purely infinite. Combining this with the result in [Je] on pure infiniteness of crossed products by finite groups, one sees that if α is an outer action by a countable abelian group G then the simple C*-algebra A ×α G is purely infinite.

Keywords

46L0546L55
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 2 , 01 June 1996 , pp. 203 - 210
Copyright
Copyright © Canadian Mathematical Society 1996

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