On the double of the Jordan plane

TL;DR

This paper investigates the structure of the Drinfeld double of the Jordan plane in characteristic zero, focusing on its simple modules and center, providing new insights into its algebraic properties.

Contribution

It explicitly computes the simple finite-dimensional modules and the center of the Drinfeld double of the Jordan plane, advancing understanding of its representation theory.

Findings

Classification of simple finite-dimensional modules

Determination of the center of the Drinfeld double

Enhanced understanding of the algebra's structure

Abstract

We compute the simple finite-dimensional modules and the center of the Drinfeld double of the Jordan plane introduced in $\texttt{arXiv:2002.02514}$ assuming that the characteristic is zero.