Which compacta are noncommutative ARs?

Details Which compacta are noncommutative ARs? Which compacta are noncommutative ARs?

2009-02-17

arxiv.org/abs/0902.3020v1

Mathematics

Operator Algebras

8 pages

Scientific paper

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.

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