Pullbacks of graph C*-algebras from admissible pushouts of graphs

Volume 120 / 2020

Piotr M. Hajac, Sarah Reznikoff, Mariusz Tobolski Banach Center Publications 120 (2020), 169-178 MSC: 46L55, 46L85. DOI: 10.4064/bc120-13

Abstract

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 $C^*(F_1\cap F_2)$.

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