The cyclic homology of k[x 1, x 2,…, x d ]/(x 1, x 2,…, x d )2

Abstract

The Hochschild homology of the ring has been known and calculated several ways. This paper uses those calculations to calculate cyclic, negative cyclic, and periodic cyclic homology of over k for These calculations have been known for or fields containing it, but this paper studies the torsion which one gets for and through it, via the universal coefficient theorem, for general k. The computations are related to homology, cohomology, and Tate cohomology of cyclic groups.