Simple Modules and Azumaya Loci over the PI quantized Weyl Algebras

TL;DR

This paper investigates the structure of multiparameter quantum Weyl algebras at roots of unity, explicitly computing their centers, PI degrees, simple modules, and Azumaya loci to deepen understanding of their algebraic properties.

Contribution

It provides explicit calculations of centers, PI degrees, simple modules, and Azumaya loci for multiparameter quantum Weyl algebras at roots of unity, advancing the algebraic theory.

Findings

Computed the center of the algebras

Determined the PI degree of the algebras

Identified the Azumaya locus

Abstract

In this article, both versions of multiparameter quantum Weyl algebras have been studied at the roots of unity. The center, PI degree, maximal-dimensional simple modules, and Azumaya locus have been explicitly computed for such algebras.