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

Published online by Cambridge University Press:  13 March 2019

JAMES GABE*
Affiliation:
School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow, G12 8SQ, Scotland e-mail: [email protected]
EFREN RUIZ
Affiliation:
Department of Mathematics, University of Hawaii, Hilo, 200 W. Kawili St., Hilo, Hawaii, 96720-4091USA e-mail: [email protected]

Abstract

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.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2019 

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