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Extensions of Quasidiagonal C*-algebras and K-theory

N. P. Brown·M. Dadarlat
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Abstract

We study the extension problem for quasidiagonal (QD) C*-algebras (i.e. when is an extension of QD C*-algebras again QD?). The main positive result states that in many instances an extension will remain QD provided that a certain boundary arising from the K-theory of the extension vanishes. A K-theoretic Hahn-Banach type property is also introduced for QD C*-algebras. We show that every nuclear QD C*-algebra has this Hahn-Banach property if and only if the extension problem for many QD C*-algebras is completely determined by a boundary map on K-theory.

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N. P. Brown, M. Dadarlat. 2000-08-23. Extensions of Quasidiagonal C*-algebras and K-theory. https://arxiv.org/abs/math/0008182

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