A Cuntz-Pimsner Model for the $C^{\ast }$-algebra of a Graph of Groups

Abstract

We provide a Cuntz-Pimsner model for graph of groups $C^{\ast }$-algebras. This allows us to compute the $K$-theory of a range of examples and show that graph of groups $C^{\ast }$-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 Poincaré duality in $KK$-theory. By constructing a $K$-theory duality class we compute the $K$-homology of these crossed products.

34 pages

References in corpus (3)

• Ideal structure of $C^{\ast }$-algebras associated with $C^{\ast }$-correspondences
• The Cayley transform in complex, real and graded $K$-theory
• C*-algebras associated to graphs of groups