Rings of $\h$-deformed differential operators

TL;DR

This paper characterizes the center of the ring of -deformed differential operators of type A and establishes an isomorphism with an extended Weyl algebra, advancing understanding of their algebraic structure.

Contribution

It provides a detailed description of the center of -deformed differential operators and links their localizations to extended Weyl algebras, revealing new structural insights.

Findings

Center of -deformed differential operators explicitly described

Isomorphism established between localizations of -deformed operators and extended Weyl algebra

Enhanced understanding of algebraic structure of -deformed differential operators

Abstract

We describe the center of the ring $\Diff(n)$ of $\h$-deformed differential operators of type A. We establish an isomorphism between certain localizations of $\Diff(n)$ and the Weyl algebra $\text{W}_n$ extended by $n$ indeterminates.