On the homogenized Weyl Algebra

TL;DR

This paper explores the relationships between categories of finitely generated modules over the homogenized Weyl algebra, the Weyl algebra, and its Yoneda algebra, providing insights at both module and derived category levels.

Contribution

It establishes new connections between these categories, enhancing understanding of their structural and homological relationships.

Findings

Relations between module categories over $B_n$, $A_n$, and $B_n^!$ are established.

Derived category relations are characterized.

Provides a framework for understanding the homological properties of these algebras.

Abstract

The aim of this paper is to give relations between the category of finetely generated graded modules over the homogeneized Weyl algebra $B_{n}$, the finetely generated modules over the Weyl algebra $A_{n}$ and the finetely generated graded modules over the Yoneda algebra $B_{n}^{!}$ of $B_{n}$. We will give these relations both at the level of the categories of modules and at the level of the derived categories.