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arXiv · 2403.02849

$C^*$-algebras associated to directed graphs of groups, and models of Kirchberg algebras

Victor Wu
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Abstract

We introduce $C^*$-algebras associated to directed graphs of groups. In particular, we associate a combinatorial $C^*$-algebra to each row-finite directed graph of groups with no sources, and show that this $C^*$-algebra is Morita equivalent to the crossed product coming from the corresponding group action on the boundary of a directed tree. Finally, we show that these $C^*$-algebras (and their Morita equivalent crossed products) contain the class of stable UCT Kirchberg algebras.

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Victor Wu. 2024-03-05. $C^*$-algebras associated to directed graphs of groups, and models of Kirchberg algebras. https://arxiv.org/abs/2403.02849

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