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arXiv · 2005.06141

A Cuntz-Pimsner Model for the $C^*$-algebra of a Graph of Groups

Alexander Mundey·Adam Rennie
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Abstract

We provide a Cuntz-Pimsner model for graph of groups $C^*$-algebras. This allows us to compute the $K$-theory of a range of examples and show that graph of groups $C^*$-algebras can be realised as Exel-Pardo algebras. We also make a preliminary investigation of whether the crossed product algebra of Baumslag-Solitar groups acting on the boundary of certain trees satisfies Poincar\'e duality in $KK$-theory. By constructing a $K$-theory duality class we compute the $K$-homology of these crossed products.

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Alexander Mundey, Adam Rennie. 2020-05-13. A Cuntz-Pimsner Model for the $C^*$-algebra of a Graph of Groups. https://doi.org/10.1016/j.jmaa.2020.124838

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