# Quantum Weyl algebras and reflection equation algebras at a root of unity

## TL;DR

This paper analyzes quantum Weyl algebras and reflection equation algebras at roots of unity, computing their centers and Azumaya loci to understand their algebraic structure and representation theory.

## Contribution

It provides explicit computations of centers and Azumaya loci for specific quantum algebras at roots of unity, illustrating broader phenomena in quantum algebra.

## Key findings

- Computed centers of quantum Weyl algebras and quantum differential operators.
- Identified Azumaya loci in these quantum algebras.
- Demonstrated elementary examples of complex quantum phenomena.

## Abstract

We compute the center and Azumaya locus in the simplest non-abelian examples of quantized multiplicative quiver varieties at a root of unity: quantum Weyl algebras of rank $N$, and quantum differential operators on the quantum group $\mathrm{GL}_2$. These examples illustrate in elementary terms much more general phenomena explored further in [Ganev-Jordan-Safronov 2019].

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Source: https://tomesphere.com/paper/1907.11005