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

2024/03/05 by Victor Wu, Wu, Victor · 1 citation
Mathematics · #20E08 (Secondary) #46L05 (Primary) #46L35 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2403.02849

openalex publication_date 2024/03/05 · openalex created_date 2024/03/07 · openalex updated_date 2026/07/28

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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• Cuntz--Pimsner algebras of partial automorphisms twisted by vector bundles II: Nuclear dimension

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