Green rings of Drinfeld Doubles of Taft algebras

TL;DR

This paper studies the structure of the Green ring of the Drinfeld double of Taft algebras, revealing it as a commutative ring generated by infinitely many elements with specific relations.

Contribution

It provides a detailed description of the Green ring of the Drinfeld double of Taft algebras, including its generators and relations, which was not previously known.

Findings

Green ring is commutative

Generated by infinitely many elements

Subject to specific algebraic relations

Abstract

In this article, we investigate the representation ring (or Green ring) of the Drinfeld double $D(H_n(q))$ of the Taft algebra $H_n(q)$, where $n$ is an integer with $n>2$ and $q$ is a root of unity of order $n$. It is shown that the Green ring $r(D(H_n(q)))$ is a commutative ring generated by infinitely many elements subject to certain relations.