An example of noncommutative deformations

TL;DR

This paper explores noncommutative deformation theory by computing deformations of modules over the first Weyl algebra, highlighting key differences from commutative deformation theory.

Contribution

It provides a specific example demonstrating unique properties of noncommutative deformation theory compared to the commutative case.

Findings

Noncommutative deformations exhibit properties distinct from commutative deformations.

The example clarifies how noncommutative deformation theory differs fundamentally.

Key properties of noncommutative deformation theory are illustrated through the Weyl algebra modules.

Abstract

We compute the noncommutative deformations of a family of modules over the first Weyl algebra. This example shows some important properties of noncommutative deformation theory that separates it from commutative deformation theory.