# Weight modules of quantized Weyl algebras

## TL;DR

This paper introduces a framework for analyzing weight modules in quantum Weyl algebras, providing classifications of simple and projective modules for two quantum versions with generic parameters.

## Contribution

It develops a general method for studying weight representations and applies it to classify modules in two quantum Weyl algebra variants.

## Key findings

- Classification of simple weight modules
- Description of projective modules
- Applicable to two quantum algebra versions

## Abstract

We develop a general framework for studying relative weight representations for certain pairs consisting of an associative algebra and a commutative subalgebra. Using these tools we describe projective and simple weight modules for quantum Weyl algebras for generic values of deformation parameters. We consider two quantum versions: one by Maltsiniotis and the other one by Akhavizadegan and Jordan.

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Source: https://tomesphere.com/paper/1812.02118