Simple modules over 3-cyclic quantum Weyl Algebra at roots of unity

TL;DR

This paper classifies simple modules of a 3-cyclic quantum Weyl algebra at roots of unity, showing it becomes a PI algebra with bounded simple module dimensions and providing a detailed description of its center.

Contribution

It systematically classifies all simple modules and computes the center of the 3-cyclic quantum Weyl algebra at roots of unity, revealing its PI algebra structure.

Findings

The algebra is a Polynomial Identity algebra at roots of unity.

Simple modules have bounded dimension by the PI degree.

Complete classification of simple modules and center computation.

Abstract

This article undertakes an exploration of simple modules of 3-cyclic quantum Weyl algebra at roots of unity. Under the roots of unity assumption, the algebra becomes a Polynomial Identity algebra and the vector space dimension of the simple modules is bounded above by its PI degree. The article systematically classifies all potential simple modules and computes the algebra's center.