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

Autor:	Mundey, Alexander, Rennie, Adam
Rok vydání:	2020
Předmět:	Mathematics - Operator Algebras Mathematics - K-Theory and Homology 46L05 (Primary) 20E08 46L80 (Secondary)
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jmaa.2020.124838
Popis:	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. Comment: 34 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2005.06141 Zobrazit plný text záznamu View this record from Arxiv