We find a substantial class of pairs of $\ast$‐homomorphisms between graph C^*‐algebras of the form $C^{\ast }(E)\hookrightarrow C^{\ast }(G)\twoheadleftarrow C^{\ast }(F)$ whose pullback C^*‐algebra is an AF graph C^*‐algebra. Our result can be interpreted as a recipe for determining the quantum space obtained by shrinking a quantum subspace. There are numerous examples from noncommutative topology, such as quantum complex projective spaces (including the standard Podleś quantum sphere) and quantum teardrops, that instantiate the result. Furthermore, to go beyond AF graph C^*‐algebras, we consider extensions of graphs over sinks and prove an analogous theorem for the thus obtained graph C^*‐algebras.

中文翻译：

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图C *代数从图的非射出推出中的非射出回撤

我们发现大量的成对的 $\ast$图C ^* -形式的代数之间的同态$C^{\ast }（Ë）\hookrightarrow C^{\ast }（G）\twoheadleftarrow C^{\ast }（F）$其回撤C ^*代数是AF图C ^*代数。我们的结果可以解释为确定通过缩小量子子空间而获得的量子空间的方法。非交换拓扑有许多实例化结果的实例，例如量子复数射影空间（包括标准的Podleś量子球）和量子泪滴。此外，要超越AF图C ^*代数，我们考虑图在汇上的扩展，并证明由此获得的图C ^*代数的一个类似定理。