Representation theory of a Class of Hopf algebras

TL;DR

This paper explores the representation theory of specific pointed Hopf algebras, showing their close relationships with well-known quantum groups and revealing new insights into their structure.

Contribution

It describes the representations of certain deformed Hopf algebras and connects them to existing quantum group representations, providing new understanding of their structure.

Findings

Representations of $U$ and $ ilde{U}$ are characterized.

Connections established with $U_q(sl(2))$ and half quantum groups.

Highlights the deformation relationship with classical quantum groups.

Abstract

The representations of the pointed Hopf algebras $U$ and $\su$ are described, where $U$ and $\su$ can be regarded as deformations of the usual quantized enveloping algebras $U_q(\mathfrak{sl}(3))$ and the small quantum groups respectively. It is illustrated that these representations have a close connection with those of the quantized enveloping algebras $U_q(\mathfrak{sl}(2))$ and those of the half quantum groups of $\mathfrak{sl}(3)$.