The Green rings of the 2-rank Taft algebra and its two relatives twisted

TL;DR

This paper explicitly describes the Green rings of the 2-rank Taft algebra and its twisted relatives, demonstrating their effectiveness in distinguishing twist-equivalent Hopf algebras.

Contribution

It provides a detailed representation-theoretic analysis of the Green rings for these Hopf algebras, revealing their utility in detecting twist equivalences.

Findings

Green rings explicitly computed for the 2-rank Taft algebra and its twisted variants

Green rings effectively distinguish twist-equivalent Hopf algebras

Representation theory techniques applied to classify algebraic structures

Abstract

In the paper, the representation rings (or the Green rings) for a family of Hopf algebras of tame type, the 2-rank Taft algebra (at $q=-1$) and its two relatives twisted by 2-cocycles are explicitly described via a representation theoretic analysis. It turns out that the Green rings can serve to detect effectively the twist-equivalent Hopf algebras here.