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

Fuente: arXiv
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Autore principale: Wu, Victor
Natura: Preprint
Pubblicazione: 2024
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author Wu, Victor
author_facet Wu, Victor
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2403_02849
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle $C^*$-algebras associated to directed graphs of groups, and models of Kirchberg algebras
Wu, Victor
Operator Algebras
46L05 (Primary), 46L35, 20E08 (Secondary)
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.
title $C^*$-algebras associated to directed graphs of groups, and models of Kirchberg algebras
topic Operator Algebras
46L05 (Primary), 46L35, 20E08 (Secondary)
url https://arxiv.org/abs/2403.02849