Tensor product decomposition rules for weight modules over the Hopf-Ore extensions of group algebras

TL;DR

This paper explicitly determines how finite dimensional weight modules over certain Hopf-Ore extensions decompose under tensor products, enriching the understanding of their module category structure.

Contribution

It provides explicit tensor product decomposition rules for all indecomposable weight modules over Hopf-Ore extensions of group algebras, under specific algebraic conditions.

Findings

Explicit tensor product decomposition rules derived

Applicable to all indecomposable weight modules

Assumes algebraically closed field of characteristic zero

Abstract

In this paper, we investigate the tensor structure of the category of finite dimensional weight modules over the Hopf-Ore extensions $kG(\chi^{-1}, a, 0)$ of group algebras $kG$. The tensor product decomposition rules for all indecomposable weight modules are explicitly given under the assumptions that $k$ is an algebraically closed field of characteristic zero, and the orders of $\chi$ and $\chi(a)$ are the same.