English

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

Operator Algebras 2021-07-27 v2 K-Theory and Homology

Abstract

We provide a Cuntz-Pimsner model for graph of groups CC^*-algebras. This allows us to compute the KK-theory of a range of examples and show that graph of groups CC^*-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 KKKK-theory. By constructing a KK-theory duality class we compute the KK-homology of these crossed products.

Keywords

Cite

@article{arxiv.2005.06141,
  title  = {A Cuntz-Pimsner Model for the $C^*$-algebra of a Graph of Groups},
  author = {Alexander Mundey and Adam Rennie},
  journal= {arXiv preprint arXiv:2005.06141},
  year   = {2021}
}

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34 pages