Weight modules over infinite dimensional Weyl algebras

TL;DR

This paper classifies simple weight modules over infinite dimensional Weyl algebras, describes their projective and injective modules, and establishes Koszulity of their blocks, advancing the understanding of their module category structure.

Contribution

It provides a complete classification of simple weight modules and describes the block structure via quivers, introducing new insights into their algebraic properties.

Findings

Classification of simple weight modules over infinite dimensional Weyl algebras

Description of indecomposable projective and injective modules

Proof of Koszulity for all blocks

Abstract

We classify simple weight modules over infinite dimensional Weyl algebras and realize them using the action on certain localizations of the polynomial ring. We describe indecomposable projective and injective weight modules and deduce from this a description of blocks of the category of weight modules by quivers and relations. As a corollary we establish Koszulity for all blocks.