Representations of the category of modules over pointed Hopf algebras over 𝕊3and 𝕊4

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...

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

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...

Doi-Hopf Modules over Weak Hopf Algebras

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