Differential Algebraic Groups
Published on 25. January 1985
272 pages
978-0-08-087433-3 (ISBN)
Description
Differential Algebraic Groups
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E.R. Kolchin
Differential Algebraic Groups
Book
01/1985
Academic Press
€102.31
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Content
- Front Cover
- Differential Algebraic Groups
- Copyright Page
- Contents
- Preface
- Acknowledgments
- Conventions
- Chapter 0. Differential Algebraic Preliminaries
- 1. Compatible homomorphisms
- 2. Numerical polynomials
- 3. Finitely generated extensions
- 4. Differential derivations
- 5. The derivation operators of a differential field
- 6. Varying the set of derivation operators
- 7. A kind of disjointness
- 8. Some groups and rings
- 9. Integrability conditions
- Chapter I. The Axioms And First Consequences
- 1. Pre differential algebraic sets
- 2. Differential algebraic groups and homogeneous differential algebraic spaces. Differential algebraic sets
- 3. The component theorem and its corollaries
- Chapter II. Variations in the Data
- 1. Varying the universal differential field
- 2. Extending the basic differential field
- 3. Varying the set of derivation operators
- Chapter III. Topology
- 1. The differential Zariski topologies
- 2. Differentially closed sets
- 3. Constrained elements
- Chapter IV. Subgroups and Homomorphisms
- 1. Differential algebraic subgroups
- 2. Differential rational homomorphisms
- 3. Direct products
- 4. Quotients
- 5. Solvable and nilpotent differential algebraic groups
- Chapter V. Mappings and Functions
- 1. Holomorphicity at a differential specialization
- 2. Differential rational mappings
- 3. Differential rational functions
- Chapter VI. Other Structures
- 1. Two lemmas
- 2. Some other differential algebraic structures
- Chapter VII. Cohomology
- 1. The differential algebraic set of a finitely generated constrained extension
- 2. Constrained cohomology
- 3. Differential rational cohomology
- 4. Differential algebraic vector spaces over u
- 5. Principal homogeneous differential algebraic spaces
- 6. Examples
- Chapter VIII. Lie Theory
- 1. Local differential rings
- 2. Tangent spaces
- 3. Differential desivations
- 4. Invariant differential derivations
- 5. The Lie algebra
- 6. Examples
- 7. Differential algebraic spaces and crossed differential rational homomorphisms
- 8. Logarithmic derivations
- 9. Further properties of logarithmic derivations
- 10. The Lie-Cassidy-Kovacic method
- 11. Images and kernels
- 12. The lie algebras of the connected differential algebraic subgroups of a connected differential algebraic group
- References
- Glossary of Notation
- Index of Definitions
