Which compacta are noncommutative ARs?

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We give a short answer to the question in the title: {\em dendrits}. Precisely we show that the $C^{\ast}$-algebra $C(X)$ of all complex-valued continuous functions on a compactum $X$ is projective in the category ${\mathcal C}^{1}$ of all (not necessarily commutative) unital $C^{\ast}$-algebras if and only if $X$ is an absolute retract of dimension $\dim X \leq 1$ or, equivalently, that $X$ is a dendrit.
8 pages

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Operator Algebras, Geometric Topology, 46M10

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http://salesiana.dossiersoluciones.com/handle/123456789/220421

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0902.3020
 http://arxiv.org/abs/0902.3020

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arXiv