UID:
almahu_9947366839702882
Format:
1 online resource (292 p.)
ISBN:
1-281-76652-6
,
9786611766528
,
0-08-087433-9
Series Statement:
Pure and Applied Mathematics
Content:
Differential algebraic groups
Note:
Includes index.
,
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
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2. Differential algebraic groups and homogeneous differential algebraic spaces. Differential algebraic sets3. 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
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5. Solvable and nilpotent differential algebraic groupsChapter 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
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Chapter VIII. Lie Theory1. 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
,
English
Additional Edition:
ISBN 0-12-417640-2
Language:
English
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