On Nichols algebras over basic Hopf algebras

Classification of Quiver Hopf Algebras and Pointed Hopf Algebras of Nichols Type

The quiver Hopf algebras are classified by means of ramification system with irreducible representations. This leads to the classification of Nichols algebras over group algebras and pointed Nichols type Hopf algebras. 2000 Mathematics Subject Classification: 16W30, 16G10 keywords: Quiver, Hopf algebra, Hopf bimodule, Nichols algebras

Doi-Hopf Modules over Weak Hopf Algebras

The theory of Doi-Hopf modules [7, 10] is generalized to Weak Hopf Algebras [1, 12, 2].

Formal groups over Hopf algebras

The aim of this section is to define some generalization of the notion of formal group. More precisely, we consider the analog of formal groups with coefficients belonging to a Hopf algebra. We also study some example of a formal group over a Hopf algebra, which generalizes the formal group of geometric cobordisms. Recently some important connections between the Landweber-Novikov algebra and th...

A Basic Introduction to Hopf Algebras

This paper offers an introduction to Hopf algebras. It is not a paper describing basic properties and applications of Hopf algebras. Rather, it is a paper providing the necessary structures in order to construct a Hopf algebra. It examines tensor products, algebras, coalgebras, bialgebras, and homology groups. After reading this paper, the reader will not be sufficiently experienced in Hopf alg...

On the Coderivations of Some Hopf Algebras