A Primer of Algebraic D-Modules
Seiten
1995
Cambridge University Press (Verlag)
978-0-521-55908-9 (ISBN)
Cambridge University Press (Verlag)
978-0-521-55908-9 (ISBN)
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.
Erscheint lt. Verlag | 29.5.1995 |
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Reihe/Serie | London Mathematical Society Student Texts |
Zusatzinfo | Worked examples or Exercises |
Verlagsort | Cambridge |
Sprache | englisch |
Maße | 152 x 229 mm |
Gewicht | 330 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
ISBN-10 | 0-521-55908-1 / 0521559081 |
ISBN-13 | 978-0-521-55908-9 / 9780521559089 |
Zustand | Neuware |
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