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arXiv · 1811.00100

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

Piotr M. Hajac·Sarah Reznikoff·Mariusz Tobolski
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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 graph $E$ is row finite and its decomposition 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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Piotr M. Hajac, Sarah Reznikoff, Mariusz Tobolski. 2018-10-31. Pullbacks of graph C*-algebras from admissible pushouts of graphs. https://arxiv.org/abs/1811.00100

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