Crossed product algebras and the homology of certain p-Adic and adélic dynamical systems

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.