A Primer of Algebraic D-Modules (London Mathematical Society Student Texts, Series Number 33)

The Theory Of D-modules Is A Rich Area Of Study Combining Ideas From Algebra And Differential Equations, And It Has Significant Applications To Diverse Areas Such As Singularity Theory And Representation Theory. This Book Introduces D-modules And Their Applications Avoiding All Unnecessary Over-sophistication. It Is Aimed At Beginning Graduate Students And The Approach Taken Is Algebraic, Concentrating On The Role Of The Weyl Algebra. Very Few Prerequisites Are Assumed, And The Book Is Virtually Self-contained. Exercises Are Included At The End Of Each Chapter And The Reader Is Given Ample References To The More Advanced Literature. This Is An Excellent Introduction To D-modules For All Who Are New To This Area. S.c. Coutinho. Includes Bibliographical References (p. [197]-202) And Index. The theory of D-modules is a rich area of study combining ideas from algebra and differential equations, and it has significant applications to diverse areas such as singularity theory and representation theory. This book introduces D-modules and their applications, avoiding all unnecessary technicalities. The author takes an algebraic approach, concentrating on the role of the Weyl algebra. The author assumes very few prerequisites, and the book is virtually self-contained. The author includes exercises at the end of each chapter and gives the reader ample references to the more advanced literature. This is an excellent introduction to D-modules for all who are new to this area. Cover; Title; Copyright; Dedication; Contents; Preface; Introduction; 1. The Weyl algebra; 2. Algebraic D-modules; 3. The book: an overview; 4. Pre-requisites; Chapter 1. The Weyl algebra; 1. Definition; 2. Canonical form; 3. Generators and relations; 4. Exercises; Chapter 2. Ideal structure of the Weyl algebra.; 1. The degree of an operator; 2. Ideal structure; 3. Positive characteristic; 4. Exercises; Chapter 3. Rings of differential operators.; 1. Definitions; 2. The Weyl algebra; 3. Exercises; Chapter 4. Jacobian Conjecture.; 1. Polynomial maps; 2. Jacobian conjecture; 3. Derivations