2000/10/10 by Rui Okayasu, Okayasu, Rui
Mathematics · #46L #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L
paper · pdf · doi:10.48550/arxiv.math/0010097
arxiv created 2000/10/10 · arxiv updated 2009/11/30
We give a construction of a nuclear C^∗-algebra associated with an amalgamated free product of groups, generalizing Spielberg's construction of a certain Cuntz-Krieger algebra associated with a finitely generated free product of cyclic groups. Our nuclear C^∗-algebras can be identified with certain Cuntz-Krieger-Pimsner algebras. We will also show that our algebras can be obtained by the crossed product construction of the canonical actions on the hyperbolic boundaries, which proves a special case of Adams' result about amenability of the boundary action for hyperbolic groups. We will also give an explicit formula of the K-groups of our algebras. Finally we will investigate the relationship between the KMS states of the generalized gauge actions on our C^∗ algebras and random walks on the groups.