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2019•Glasgow Mathematical JournalRequires access

THE UNITAL EXT-GROUPS AND CLASSIFICATION OFC*-ALGEBRAS

James Gabe, Efren Ruiz

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Abstract

Abstract The semigroups of unital extensions of separableC*-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 obtainK-theoretic classification of both unital and non-unital extensions ofC*-algebras, and in particular we obtain a completeK-theoretic classification of full extensions of UCT Kirchberg algebras by stable AF algebras.

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Abstract The semigroups of unital extensions of separableC*-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 obtainK-theoretic classification of both unital and non-unital extensions ofC*-algebras, and in particular we obtain a completeK-theoretic classification of full extensions of UCT Kirchberg algebras by stable AF algebras.

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Available abstract

Abstract The semigroups of unital extensions of separableC*-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 obtainK-theoretic classification of both unital and non-unital extensions ofC*-algebras, and in particular we obtain a completeK-theoretic classification of full extensions of UCT Kirchberg algebras by stable AF algebras.

Key concepts: Unital, Mathematics, Separable space, Invertible matrix, Pure mathematics, Algebra over a field, Mathematical analysis

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