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 -algebras. This allows us to compute the -theory of a range of examples and show that graph of groups -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 -theory. By constructing a -theory duality class we compute the -homology of these crossed products.
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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