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$C^*$-algebras associated to directed graphs of groups, and models of Kirchberg algebras (2403.02849v1)

Published 5 Mar 2024 in math.OA

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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