Complete reducibility theorems for modules over pointed Hopf algebras

TL;DR

This paper studies the representation theory of pointed Hopf algebras, classifies simple modules, and proves a complete reducibility theorem, extending previous results in the field.

Contribution

It provides a comprehensive classification of simple modules and a complete reducibility theorem for a broad class of pointed Hopf algebras, advancing the understanding of their module categories.

Findings

Classification of all simple modules in the category

Determination of weight multiplicities

Establishment of complete reducibility theorem

Abstract

We investigate the representation theory of a large class of pointed Hopf algebras, extending results of Lusztig and others. We classify all simple modules in a suitable category and determine the weight multiplicities; we establish a complete reducibility theorem in this category.