Cyclic homology of monogenic extensions
Let D be a commutative k-algebra and S a multiplicative subset of k[X]. After defining mixed complexes and strongly homotopy k-maps, the authors prove that for \(A=k[X]/<X^ n>\), where k is a commutative ring with identity, the double complex \(B(A)_{norm}\) defined by Loday and Quillen can be replaced by an easier complex. This leads to a computation of the cyclic homology of \(D[X]/<X^ n>\) and \(S^{-1}D[X]\) in terms of the cyclic and Hochschild homology of D, where D is a k-algebra with k a commutative ring containing a field. Similar results are obtained for cohomology. Finally, when k is a field, the authors compute the cyclic homology and cohomology of D[X \(]/ \), with P a polynomial in k[X]. These results are obtained without assuming characteristic zero.
scientific article; zbMATH DE number 4152542