A Primer of Algebraic D-Modulesby S. C. Coutinho, Coutinho S. C.
Pub. Date: 09/28/1995
Publisher: Cambridge University Press
Combining ideas from algebra and differential equations, the theory of D-modules is a rich area of study with significant applications to diverse areas such as singularity theory and representation theory. This text introduces D-modules and their applications.
Table of Contents1. 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.
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