The cyclic homology of affine algebras

Abstract

In this paper, we study the cyclic homology of affine algebras over a field of characteristic 0. We show that if A is such an algebra the inverse system ( HC *+2m (A),S) m decomposes in sufficiently large degrees into the direct sum of the constant system with value ⊕ l∈Z H inf *+21 (A) and a system which is essentially zero. The essentially zero component is the kernel of the Loday-Quillen map μ and the behavior of the restriction of S on it is closely related to the degeneracy of the spectral sequence associated with Connes' exact couple of A .