On the automorphisms of quantum Weyl algebras

TL;DR

This paper investigates the automorphisms of quantum Weyl algebras, addressing quantum analogues of classical algebraic conjectures and problems, with results applicable to various quantum algebra families.

Contribution

It establishes quantum versions of the Jacobian conjecture and Tame Generators problem for specific quantum Weyl algebra analogues, expanding understanding of their automorphism groups.

Findings

Proves quantum Jacobian conjecture for certain quantum Weyl algebras

Demonstrates automorphism classification for Weyl-Hayashi algebras

Extends results to tensor powers of quantized Weyl algebra variants

Abstract

Motivated by Weyl algebra analogues of the Jacobian conjecture and the Tame Generators problem, we prove quantum versions of these problems for a family of analogues to the Weyl algebras. In particular, our results cover the Weyl-Hayashi algebras and tensor powers of a quantization of the first Weyl algebra which arises as a primitive factor algebra of $U_q^+(\mathfrak{so}_5)$.