The Homology of Cyclic Products

The Homology of Cyclic Products

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...

Free Products, Cyclic Homology, and the Gauss-manin Connection

We present a new approach to cyclic homology that does not involve Connes’ differential and is based on (Ω q A)[u], d + u · ı∆, a noncommutative equivariant de Rham complex of an associative algebra A. Here d is the Karoubi-de Rham differential, which replaces the Connes differential, and ı∆ is an operation analogous to contraction with a vector field. As a byproduct, we give a simple explicit ...

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...

The Generalized Homology of Products

We construct a spectral sequence that computes the generalized homology E∗( Q Xα) of a product of spectra. The E2-term of this spectral sequence consists of the right derived functors of product in the category of E∗E-comodules, and the spectral sequence always converges when E is the Johnson-Wilson theory E(n) and the Xα are Ln-local. We are able to prove some results about the E2-term of this...