Dipper Donkin Quantized Matrix Algebra and Reflection Equation Algebra at root of unity

TL;DR

This paper studies quantized matrix algebras at roots of unity, classifies simple modules for rank 2 cases, and explores finite dimensional indecomposable modules, advancing understanding of their representation theory.

Contribution

It provides a complete classification of simple modules and constructs certain indecomposable modules for quantized matrix algebras at roots of unity.

Findings

Classification of simple modules for rank 2 algebras

Construction of finite dimensional indecomposable modules

Enhanced understanding of module structures at roots of unity

Abstract

In this article the quantized matrix algebras as in the title have been studied at a root of unity. A full classification of simple modules over such quantized matrix algebras of rank $2$ along with a class of finite dimensional indecomposable modules are given.