Bass--Serre trees of amalgamated free product C*-algebras

2016/09/28 by Kei Hasegawa, Hasegawa, Kei · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1609.08837

openalex publication_date 2016/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any reduced amalgamated free product C^*-algebra (A,E)=(A₁, E₁) ∗_D (A₂,E₂), we introduce and study a canonical ambient C^*-algebra ΔT(A,E) of A which generalizes the crossed product arising from the canonical action of an amalgamated free product group on the compactification of the associated Bass--Serre tree. Using an explicit identification of ΔT(A,E) with a Cuntz--Pimsner algebra we prove two kinds of "amenability" results for ΔT(A,E); nuclearity and universality. As applications of our framework, we provide new conceptual, and simpler proofs of several known theorems on approximation properties, embeddability, and KK-theory for reduced amalgamated free product C^*-algebras.

Citations

• The KK-Theory of Fundamental C*-Algebras

Cited by

• Universal C^∗-Algebras from Graph Products: Structure and Applications

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