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THE UNITAL EXT-GROUPS AND CLASSIFICATION OF C*-ALGEBRAS

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  13 March 2019

JAMES GABE Open the ORCID record for JAMES GABE [Opens in a new window]  and
EFREN RUIZ
JAMES GABE*
Affiliation:
School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow, G12 8SQ, Scotland e-mail: jamiegabe123@hotmail.com
EFREN RUIZ
Affiliation:
Department of Mathematics, University of Hawaii, Hilo, 200 W. Kawili St., Hilo, Hawaii, 96720-4091USA e-mail: ruize@hawaii.edu
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Abstract

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The semigroups of unital extensions of separable C*-algebras come in two flavours: a strong and a weak version. By the unital Ext-groups, we mean the groups of invertible elements in these semigroups. We use the unital Ext-groups to obtain K-theoretic classification of both unital and non-unital extensions of C*-algebras, and in particular we obtain a complete K-theoretic classification of full extensions of UCT Kirchberg algebras by stable AF algebras.

MSC classification

Primary: 46L35: Classifications of $C^*$-algebras
Secondary: 46L80: $K$-theory and operator algebras (including cyclic theory)

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 1 , January 2020 , pp. 201 - 231
Copyright
Copyright © Glasgow Mathematical Journal Trust 2019 

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