Crossed Product Algebras and the Homology of Certain p-Adic and Adélic Dynamical Systems

Leichtnam, Eric
Nistor, Victor

¹Institut de Jussieu, CNRS, UMR 7586, Aile 46.0, 3^eme Etage, 4 Place Jussieu, 75005, Paris, France, e-mail: [email protected]
²Pennsylvania State University, Math. Dept., University Park, PA 16802, USA, e-mail: [email protected]

K-Theory 21(1):p 1-23, September 2000.

We identify the Hochschild, cyclic, and periodic cyclic homology groups of dynamical systems algebras arising from the action of Q^* on the spaces of finite and infinite adéles of Q. In the process, we establish several results on the homology of the space of functions on a locally compact, totally disconnected space and its crossed products. Then we use these results to compute the homology groups of the Bost–Connes algebra.