Notes on Weyl Algebra and D-Modules

Abstract

Weyl algebras, sometimes called algebras of differential operators, are a fascinating and important subject, which relates Non-Commutative and Commutative Algebra, Algebraic Geometry and Analysis in very appealing way. The theory of modules over Weyl algebras, sometimes called D-modules, finds application in the theory of partial differential equations, and thus has a great impact to many fields of Mathematics. In our course, we shall give a short introduction to the subject, using only prerequisites from Linear Algebra, Basic Abstract Algebra, and Basic Commutative Algebra. In addition, in the last two sections, we present a few recent results.