Indecomposable decomposition of tensor products of modules over Drinfeld Doubles of Taft algebras

TL;DR

This paper explicitly describes how tensor products of all indecomposable modules decompose in the category of finite-dimensional representations of Drinfeld doubles of Taft algebras, advancing understanding of their tensor structure.

Contribution

It provides explicit decomposition rules for tensor products of all finite-dimensional indecomposable modules over Drinfeld doubles of Taft algebras.

Findings

Explicit tensor product decomposition rules are established.

Complete classification of indecomposable modules is utilized.

Enhances understanding of the tensor structure in these categories.

Abstract

In this paper, we study the tensor structure of category of finite dimensional representations of Drinfeld quantum doubles $D(H_n(q))$ of Taft Hopf algebras $H_n(q)$. Tensor product decomposition rules for all finite dimensional indecomposable modules are explicitly given.