Locally finite representations over Noetherian Hopf algebras

Noetherian Hopf Algebras

This short survey article reviews our current state of understanding of the structure of noetherian Hopf algebras. The focus is on homological properties. A number of open problems are listed. To the memory of my teacher and friend Brian Hartley

Representations of Finite Dimensional Pointed Hopf Algebras over S 3

The classification of finite-dimensional pointed Hopf algebras with group S3 was finished in [AHS]: there are exactly two of them, the bosonization of a Nichols algebra of dimension 12 and a non-trivial lifting. Here we determine all simple modules over any of these Hopf algebras. We also find the Gabriel quivers, the projective covers of the simple modules, and prove that they are not of finit...

Representations of Finite Dimensional Hopf Algebras

Let H denote a nite dimensional Hopf algebra with antipode S over a eld |. We give a new proof of the fact, due to Oberst and Schneider OS], that H is a symmetric algebra if and only if H is unimodular and S 2 is inner. If H is involutory and not semisimple, then the dimensions of all projective H-modules are shown to be divisible by char|. In the case where |is a splitting eld for H , we give ...

Finite Dimensional Pointed Hopf Algebras over S

Induced Representations of Hopf Algebras

Hopf representation is a module and comodule with a consistency condition that is more general than the consistency condition of Hopf modules. For a Hopf algebra H, we construct an induced Hopf representation from a representation of a bialgebra B using a bialgebra epimorphism π : H → B. Application on the quantum group Eq(2) is given. Mathematics Subject Classification: 16T05, 06B15, 17B37