On pointed Hopf algebras over nilpotent groups

Pointed Hopf Algebras over Non-abelian Groups

The class of finite-dimensional pointed Hopf algebras is a field of current active research. The classification of these algebras has seen substantial progress since the development of the so-called “Lifting method” by Andruskiewitsch and Schneider. With this tool, the case in which the group of group-like elements is abelian is almost completed and recent results by these and other authors suc...

Module Categories over Pointed Hopf Algebras

We develop some techniques for studying exact module categories over some families of pointed finite-dimensional Hopf algebras. As an application we classify exact module categories over the tensor category of representations of the small quantum groups uq(sl2).

Finite Dimensional Pointed Hopf Algebras over S

On Pointed Hopf Algebras with Weyl Groups of Exceptional Type

All −1-type pointed Hopf algebras with Weyl groups of exceptional type are found. It is proved that every non −1-type pointed Hopf algebra is infinite dimensional. 2000 Mathematics Subject Classification: 16W30, 16G10 keywords: Quiver, Hopf algebra, Weyl group.

On Pointed Hopf Algebras with Classical Weyl Groups

Many cases of infinite dimensional Nichols algebras of irreducible YetterDrinfeld modules over classical Weyl groups are found. It is proved that except a few cases Nichols algebras of reducible Yetter-Drinfeld modules over classical Weyl groups are infinite dimensional. Some finite dimensional Nichols algebras of Yetter-Drinfeld modules over classical Weyl groups are given.