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Pullbacks of graph C*-algebras from admissible pushouts of graphs. (English) Zbl 1465.46049

Dąbrowski, Ludwik (ed.) et al., Quantum dynamics. Dedicated to Professor Paul Baum. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Cent. Publ. 120, 169-178 (2020).
Summary: We define an admissible decomposition of a graph \(E\) into subgraphs \(F_1\) and \(F_2\), and consider the intersection graph \(F_1\cap F_2\) as a subgraph of both \(F_1\) and \(F_2\). We prove that, if the decomposition of the graph \(E\) into the subgraphs \(F_1\) and \(F_2\) is admissible, then the graph C*-algebra \(C^*(E)\) of \(E\) is the pullback C*-algebra of the canonical surjections from \(C^*(F_1)\) and \(C^*(F_2)\) onto \(C^*(F_1\cap F_2)\).
For the entire collection see [Zbl 1462.46002].

MSC:

46L05 General theory of \(C^*\)-algebras
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References:

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