THE CYCLIC HOMOLOGY OF AFFINE ALGEBRAS

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 +H-l is an element of Z(inf)*(+2l)(A) and a system which is essentially zero. The essentially zero component is the kernel of the Loday-Quillen map mu 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.