A Primer of Algebraic D-Modules

This book introduces D-modules and their applications avoiding all unnecessary over-sophistication.

S. C. Coutinho (Author)

9780521559089, Cambridge University Press

Paperback, published 29 May 1995

220 pages
22.9 x 15.2 x 1.3 cm, 0.33 kg

'A readable account.' Mathematika

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.

1. The Weyl algebra
2. Ideal structure of the Weyl algebra
3. Rings of differential operators
4. Jacobian conjectures
5. Modules over the Weyl algebra
6. Differential equations
7. Graded and filtered modules
8. Noetherian rings and modules
9. Dimension and multiplicity
10. Holonomic modules
11. Characteristic varieties
12. Tensor products
13. External products
14. Inverse image
15. Embeddings
16. Direct images
17. Kashiwara's theorem
18. Preservation of holonomy
19. Stability of differential equations
20. Automatic proof of identities.

Subject Areas: Algebra [PBF]