Quantum Weyl algebras

TL;DR

This paper explores the algebraic structure and deformation properties of quantum Weyl algebras associated with Hecke symmetries, providing insights into their ring-theoretic aspects and specific cases.

Contribution

It introduces a general framework for the ring-theoretic analysis of quantum Weyl algebras and examines their relation to formal deformations of classical Weyl algebras.

Findings

Characterization of ring-theoretic properties of $A_n(R)$

Connections between quantum Weyl algebras and formal deformations

Analysis of specific quantum Weyl algebras from well-known Hecke symmetries

Abstract

For any Hecke symmetry $R$ there is a natural quantization $A_n(R)$ of the Weyl algebra $A_n$. The aim of this paper is to study some general ring-theoretic aspects of $A_n(R)$ and its relations to formal deformations of $A_n$. We also obtain further information on those quantizations obtained from some well-known Hecke symmetries.