Cyclic homology of group rings

Cyclic Group Actions on Polynomial Rings

We consider a cyclic group of order p acting on a module incharacteristic p and show how to reduce the calculation of the symmetric algebra to that of the exterior algebra. Consider a cyclic group of order p acting on a polynomial ring S = k[x1, . . . , xr], where k is a field of characteristic p; this is equivalent to the symmetric algebra S∗(V ) on the module V generated by x1, . . . , xr. We...

On the cyclic Homology of multiplier Hopf algebras

In this paper, we will study the theory of cyclic homology for regular multiplier Hopf algebras. We associate a cyclic module to a triple $(mathcal{R},mathcal{H},mathcal{X})$ consisting of a regular multiplier Hopf algebra $mathcal{H}$, a left $mathcal{H}$-comodule algebra $mathcal{R}$, and a unital left $mathcal{H}$-module $mathcal{X}$ which is also a unital algebra. First, we construct a para...

Cyclic homology and equivariant homology

The purpose of this paper is to explore the relationship between the cyclic homology and cohomology theories of Connes [9-11], see also Loday and Quillen [20], and "IF equivariant homology and cohomology theories. Here II" is the circle group. The most general results involve the definitions of the cyclic homology of cyclic chain complexes and the notions of cyclic and cocyclic spaces so precis...

On the Cyclic Homology of Commutative Algebras over Arbitrary Ground Rings

On the Cyclic Homology of Commutative Algebras over Arbitrary Ground Rings

The algebra ΛV ⊗ Γ(dV ) is a divided power version of the de Rham algebra; in the particular case when k is a field of characteristic zero, the spectral sequences above agree with those found in [BuV], where it is shown they degenerate at the E term. For arbitrary ground rings we prove here (theorem 2.3) that if Vn = 0 for n ≥ 2 then E = E. From this we derive a formula for the Hochschild homol...