A primer of algebraic D-modules /:
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-soph...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [England] ; New York, NY, USA :
Cambridge University Press,
1995.
|
| Schriftenreihe: | London Mathematical Society student texts ;
33. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xii, 207 pages) |
| Bibliographie: | Includes bibliographical references (pages 197-202) and index. |
| ISBN: | 9781107362352 1107362350 9780511623653 0511623658 |
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| 520 | |a 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. | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 4. Automorphisms5. Exercises; Chapter 5. Modules over the Weyl algebra.; 1. The polynomial ring; 2. Twisting; 3. Holomorphic functions; 4. Exercises; Chapter 6. Differential equations.; 1. The D-module of an equation; 2. Direct limit of modules; 3. Microfunctions; 4. Exercises; Chapter 7. Graded and filtered modules.; 1. Graded rings; 2. Filtered rings; 3. Associated graded algebra; 4. Filtered modules; 5. Induced filtration; 6. Exercises; Chapter 8. Noetherian rings and modules.; 1. Noetherian modules; 2. Noetherian rings; 3. Good filtration; 4. Exercises | |
| 505 | 8 | |a Chapter 9. Dimension and multiplicity. 1. The Hilbert polynomial; 2. Dimension and multiplicity; 3. Basic properties; 4. Bernstein's inequality; 5. Exercises; Chapter 10. Holonomic modules.; 1. Definition and examples; 2. Basic properties; 3. Further examples; 4. Exercises; Chapter 11. Characteristic varieties.; 1. The characteristic variety; 2. Symplectic geometry; 3. Non-holonomic irreducible modules; 4. Exercises; Chapter 12. Tensor products.; 1. Bimodules; 2. Tensor products; 3. The universal property; 4. Basic properties; 5. Localization; 6. Exercises; Chapter 13. External products. | |
| 505 | 8 | |a 1. External products of algebras2. External products of modules; 3. Graduations and filtrations; 4. Dimensions and multiplicities; 5. Exercises; Chapter 14. Inverse Image.; 1. Change of rings; 2. Inverse images; 3. Projections; 4. Exercises; Chapter 15. Embeddings.; 1. The standard embedding; 2. Composition; 3. Embeddings revisited; 4. Exercises; Chapter 16. Direct images; 1. Right modules; 2. Transposition; 3. Left modules; 4. Exercises; Chapter 17. Kashiwara's theorem; 1. Embeddings; 2. Kashiwara's theorem; 3. Exercises; Chapter 18. Preservation of holonomy.; 1. Inverse images | |
| 505 | 8 | |a 2. Direct images3. Categories and functors; 4. Exercises; Chapter 19. Stability of differential equations.; 1. Asymptotic stability; 2. Global upper bound; 3. Global stability on the plane; 4. Exercises; Chapter 20. Automatic proof of identities.; 1. Holonomic functions; 2. Hyperexponential functions; 3. The method; 4. Exercises; Coda; Appendix 1. Defining the action of a module using generators; Appendix 2. Local inversion theorem; References; Index | |
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| contents | 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 4. Automorphisms5. Exercises; Chapter 5. Modules over the Weyl algebra.; 1. The polynomial ring; 2. Twisting; 3. Holomorphic functions; 4. Exercises; Chapter 6. Differential equations.; 1. The D-module of an equation; 2. Direct limit of modules; 3. Microfunctions; 4. Exercises; Chapter 7. Graded and filtered modules.; 1. Graded rings; 2. Filtered rings; 3. Associated graded algebra; 4. Filtered modules; 5. Induced filtration; 6. Exercises; Chapter 8. Noetherian rings and modules.; 1. Noetherian modules; 2. Noetherian rings; 3. Good filtration; 4. Exercises Chapter 9. Dimension and multiplicity. 1. The Hilbert polynomial; 2. Dimension and multiplicity; 3. Basic properties; 4. Bernstein's inequality; 5. Exercises; Chapter 10. Holonomic modules.; 1. Definition and examples; 2. Basic properties; 3. Further examples; 4. Exercises; Chapter 11. Characteristic varieties.; 1. The characteristic variety; 2. Symplectic geometry; 3. Non-holonomic irreducible modules; 4. Exercises; Chapter 12. Tensor products.; 1. Bimodules; 2. Tensor products; 3. The universal property; 4. Basic properties; 5. Localization; 6. Exercises; Chapter 13. External products. 1. External products of algebras2. External products of modules; 3. Graduations and filtrations; 4. Dimensions and multiplicities; 5. Exercises; Chapter 14. Inverse Image.; 1. Change of rings; 2. Inverse images; 3. Projections; 4. Exercises; Chapter 15. Embeddings.; 1. The standard embedding; 2. Composition; 3. Embeddings revisited; 4. Exercises; Chapter 16. Direct images; 1. Right modules; 2. Transposition; 3. Left modules; 4. Exercises; Chapter 17. Kashiwara's theorem; 1. Embeddings; 2. Kashiwara's theorem; 3. Exercises; Chapter 18. Preservation of holonomy.; 1. Inverse images 2. Direct images3. Categories and functors; 4. Exercises; Chapter 19. Stability of differential equations.; 1. Asymptotic stability; 2. Global upper bound; 3. Global stability on the plane; 4. Exercises; Chapter 20. Automatic proof of identities.; 1. Holonomic functions; 2. Hyperexponential functions; 3. The method; 4. Exercises; Coda; Appendix 1. Defining the action of a module using generators; Appendix 2. Local inversion theorem; References; Index |
| ctrlnum | (OCoLC)831664169 |
| dewey-full | 512/.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.4 |
| dewey-search | 512/.4 |
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:14Z |
| institution | BVB |
| isbn | 9781107362352 1107362350 9780511623653 0511623658 |
| language | English |
| oclc_num | 831664169 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xii, 207 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society student texts ; |
| series2 | London Mathematical Society student texts ; |
| spelling | Coutinho, S. C. A primer of algebraic D-modules / S.C. Coutinho. Cambridge [England] ; New York, NY, USA : Cambridge University Press, 1995. 1 online resource (xii, 207 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society student texts ; 33 Includes bibliographical references (pages 197-202) and index. Print version record. 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. 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 4. Automorphisms5. Exercises; Chapter 5. Modules over the Weyl algebra.; 1. The polynomial ring; 2. Twisting; 3. Holomorphic functions; 4. Exercises; Chapter 6. Differential equations.; 1. The D-module of an equation; 2. Direct limit of modules; 3. Microfunctions; 4. Exercises; Chapter 7. Graded and filtered modules.; 1. Graded rings; 2. Filtered rings; 3. Associated graded algebra; 4. Filtered modules; 5. Induced filtration; 6. Exercises; Chapter 8. Noetherian rings and modules.; 1. Noetherian modules; 2. Noetherian rings; 3. Good filtration; 4. Exercises Chapter 9. Dimension and multiplicity. 1. The Hilbert polynomial; 2. Dimension and multiplicity; 3. Basic properties; 4. Bernstein's inequality; 5. Exercises; Chapter 10. Holonomic modules.; 1. Definition and examples; 2. Basic properties; 3. Further examples; 4. Exercises; Chapter 11. Characteristic varieties.; 1. The characteristic variety; 2. Symplectic geometry; 3. Non-holonomic irreducible modules; 4. Exercises; Chapter 12. Tensor products.; 1. Bimodules; 2. Tensor products; 3. The universal property; 4. Basic properties; 5. Localization; 6. Exercises; Chapter 13. External products. 1. External products of algebras2. External products of modules; 3. Graduations and filtrations; 4. Dimensions and multiplicities; 5. Exercises; Chapter 14. Inverse Image.; 1. Change of rings; 2. Inverse images; 3. Projections; 4. Exercises; Chapter 15. Embeddings.; 1. The standard embedding; 2. Composition; 3. Embeddings revisited; 4. Exercises; Chapter 16. Direct images; 1. Right modules; 2. Transposition; 3. Left modules; 4. Exercises; Chapter 17. Kashiwara's theorem; 1. Embeddings; 2. Kashiwara's theorem; 3. Exercises; Chapter 18. Preservation of holonomy.; 1. Inverse images 2. Direct images3. Categories and functors; 4. Exercises; Chapter 19. Stability of differential equations.; 1. Asymptotic stability; 2. Global upper bound; 3. Global stability on the plane; 4. Exercises; Chapter 20. Automatic proof of identities.; 1. Holonomic functions; 2. Hyperexponential functions; 3. The method; 4. Exercises; Coda; Appendix 1. Defining the action of a module using generators; Appendix 2. Local inversion theorem; References; Index D-modules. http://id.loc.gov/authorities/subjects/sh92006437 D-modules. MATHEMATICS Algebra Intermediate. bisacsh D-modules fast D-Modul gnd http://d-nb.info/gnd/4305548-5 Weyl-Algebra gnd http://d-nb.info/gnd/4373964-7 Anneaux (algèbre) ram D-modules, Théorie des. ram has work: A primer of algebraic D-modules (Text) https://id.oclc.org/worldcat/entity/E39PCXvh6PyWJRDjfq6JkGwRVd https://id.oclc.org/worldcat/ontology/hasWork Print version: Coutinho, S.C. Primer of algebraic D-modules. Cambridge [England] ; New York, NY, USA : Cambridge University Press, 1995 0521551196 (DLC) 95006628 (OCoLC)32168267 London Mathematical Society student texts ; 33. http://id.loc.gov/authorities/names/n84727069 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=551346 Volltext |
| spellingShingle | Coutinho, S. C. A primer of algebraic D-modules / London Mathematical Society student texts ; 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 4. Automorphisms5. Exercises; Chapter 5. Modules over the Weyl algebra.; 1. The polynomial ring; 2. Twisting; 3. Holomorphic functions; 4. Exercises; Chapter 6. Differential equations.; 1. The D-module of an equation; 2. Direct limit of modules; 3. Microfunctions; 4. Exercises; Chapter 7. Graded and filtered modules.; 1. Graded rings; 2. Filtered rings; 3. Associated graded algebra; 4. Filtered modules; 5. Induced filtration; 6. Exercises; Chapter 8. Noetherian rings and modules.; 1. Noetherian modules; 2. Noetherian rings; 3. Good filtration; 4. Exercises Chapter 9. Dimension and multiplicity. 1. The Hilbert polynomial; 2. Dimension and multiplicity; 3. Basic properties; 4. Bernstein's inequality; 5. Exercises; Chapter 10. Holonomic modules.; 1. Definition and examples; 2. Basic properties; 3. Further examples; 4. Exercises; Chapter 11. Characteristic varieties.; 1. The characteristic variety; 2. Symplectic geometry; 3. Non-holonomic irreducible modules; 4. Exercises; Chapter 12. Tensor products.; 1. Bimodules; 2. Tensor products; 3. The universal property; 4. Basic properties; 5. Localization; 6. Exercises; Chapter 13. External products. 1. External products of algebras2. External products of modules; 3. Graduations and filtrations; 4. Dimensions and multiplicities; 5. Exercises; Chapter 14. Inverse Image.; 1. Change of rings; 2. Inverse images; 3. Projections; 4. Exercises; Chapter 15. Embeddings.; 1. The standard embedding; 2. Composition; 3. Embeddings revisited; 4. Exercises; Chapter 16. Direct images; 1. Right modules; 2. Transposition; 3. Left modules; 4. Exercises; Chapter 17. Kashiwara's theorem; 1. Embeddings; 2. Kashiwara's theorem; 3. Exercises; Chapter 18. Preservation of holonomy.; 1. Inverse images 2. Direct images3. Categories and functors; 4. Exercises; Chapter 19. Stability of differential equations.; 1. Asymptotic stability; 2. Global upper bound; 3. Global stability on the plane; 4. Exercises; Chapter 20. Automatic proof of identities.; 1. Holonomic functions; 2. Hyperexponential functions; 3. The method; 4. Exercises; Coda; Appendix 1. Defining the action of a module using generators; Appendix 2. Local inversion theorem; References; Index D-modules. http://id.loc.gov/authorities/subjects/sh92006437 D-modules. MATHEMATICS Algebra Intermediate. bisacsh D-modules fast D-Modul gnd http://d-nb.info/gnd/4305548-5 Weyl-Algebra gnd http://d-nb.info/gnd/4373964-7 Anneaux (algèbre) ram D-modules, Théorie des. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh92006437 http://d-nb.info/gnd/4305548-5 http://d-nb.info/gnd/4373964-7 |
| title | A primer of algebraic D-modules / |
| title_auth | A primer of algebraic D-modules / |
| title_exact_search | A primer of algebraic D-modules / |
| title_full | A primer of algebraic D-modules / S.C. Coutinho. |
| title_fullStr | A primer of algebraic D-modules / S.C. Coutinho. |
| title_full_unstemmed | A primer of algebraic D-modules / S.C. Coutinho. |
| title_short | A primer of algebraic D-modules / |
| title_sort | primer of algebraic d modules |
| topic | D-modules. http://id.loc.gov/authorities/subjects/sh92006437 D-modules. MATHEMATICS Algebra Intermediate. bisacsh D-modules fast D-Modul gnd http://d-nb.info/gnd/4305548-5 Weyl-Algebra gnd http://d-nb.info/gnd/4373964-7 Anneaux (algèbre) ram D-modules, Théorie des. ram |
| topic_facet | D-modules. MATHEMATICS Algebra Intermediate. D-modules D-Modul Weyl-Algebra Anneaux (algèbre) D-modules, Théorie des. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=551346 |
| work_keys_str_mv | AT coutinhosc aprimerofalgebraicdmodules AT coutinhosc primerofalgebraicdmodules |