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Ext and OrderExt Classes of Certain Automorphisms of C*-Algebras Arising from Cantor Minimal Systems

Published online by Cambridge University Press:  20 November 2018

Hiroki Matui
Hiroki Matui*
Affiliation:
Department of Mathematics University of Kyoto Kitasirakawa-Oiwaketyô, Sakyôku Kyôto, 606-8502 Japan, email: matui@kusm.kyoto-u.ac.jp
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Abstract

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Giordano, Putnam and Skau showed that the transformation group ${{C}^{*}}$ -algebra arising from a Cantor minimal system is an $AT$ -algebra, and classified it by its $K$ -theory. For approximately inner automorphisms that preserve $C\left( X \right)$ , we will determine their classes in the Ext and OrderExt groups, and introduce a new invariant for the closure of the topological full group. We will also prove that every automorphism in the kernel of the homomorphism into the Ext group is homotopic to an inner automorphism, which extends Kishimoto’s result.

Keywords

46L4046L8054H20

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 53 , Issue 2 , 01 April 2001 , pp. 325 - 354
Copyright
Copyright © Canadian Mathematical Society 2001

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