Buch, Englisch, Band 33, 219 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 515 g
Buch, Englisch, Band 33, 219 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 515 g
Reihe: London Mathematical Society Student Texts
ISBN: 978-0-521-55119-9
Verlag: Cambridge University Press
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.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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.
