Noncommutative Galois Extension and Graded q-Differential Algebra

On a graded q-differential algebra

We construct the graded q-differential algebra on a ZN -graded algebra by means of a graded q-commutator. We apply this construction to a reduced quantum plane and study the first order differential calculus on a reduced quantum plane induced by the N -differential of the graded q-differential algebra. 1 Graded q-differential algebra In this section given a ZN -graded algebra we construct the g...

Differential Graded Algebra

Differential Graded Algebra

Hz-algebra Spectra Are Differential Graded Algebras

We construct Quillen equivalences on the Quillen model categories of rings, modules and algebras over Z-graded chain complexes and HZ-module spectra. A Quillen equivalence of Quillen model categories is the most highly structured notion of equivalence between homotopy theories. We use these equivalences in turn to produce algebraic models for rational stable model categories.

Homotopic Hopf-Galois extensions of commutative differential graded algebras

This thesis is concerned with the definition and the study of properties of homotopic Hopf-Galois extensions in the category Ch 0 k of chain complexes over a field k, equipped with its projective model structure. Given a differential graded k-Hopf algebra H of finite type, we define a homotopic H-Hopf-Galois extension to be a morphism ' : B ! A of augmented H-comodule dg-k-algebras, where B is ...