Notes on Weyl Algebra and D-Modules

  • Markus BrodmannEmail author
Part of the Lecture Notes in Mathematics book series (LNM, volume 2210)


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.



(1) The author expresses his gratitude toward the VIASM and the Mathematical Institute of the Vietnam Academy of Science and Technology MIVAST in Hanoi for the invitation and generous financial and institutional support during his stay in Vietnam in October–December 2013, but also toward the Universities of Thai Nguyen, of Hué and toward the Ho Chi Minh City University of Education for their intermediate invitations and financial support.

(2) The author expresses his gratitude toward the Indian National Centre for Mathematics of IIT-B and TIFR-Mumbai and toward St. Joseph’s College in Irinjalakude, Kerala, India for their financial and institutional support during his visit in June-July 2016.

(3) In particular, the author to thanks to the referee, for his very careful and critical study of the manuscript, for his valuable historical and bibliographical hints—in particular to the paper [2] (see Conclusive Remark 1.14.10 (C))—and for his suggestions which helped to improve and clarify a number of arguments, and also for his long list of misprints.


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Authors and Affiliations

  1. 1.Universität Zürich, Institut für MathematikZürichSwitzerland

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