Algebraic Theory of Locally Nilpotent Derivations (Encyclopaedia of Mathematical Sciences)
Edition: 1 edition
Publisher: Springer
Published: October 19, 2006
Language: eng
Format: Hardcover
Number of pages: 261
ISBN-13: 9783540295211
Subjects: Algebra; Mathematics; Science/Mathematics; Algebra - General; Geometry - Algebraic; Group Theory; Mathematics / Algebra / General; additive group action on affine varieties; invariant theory; locally nilpotent derivation
First sentence: The study of locally nipotent derivations and Ga-actions has recently emerged from the long shadows of other branches of mathematics, branches whose provenance is older and more distinguished.
Description: But, in the further development of a branch of mathematics, the human mind, encouraged by the success of its solutions, becomes conscious of its independence. It evolves from itself alone, often without appreciable in?uence from without, by means of logical combination, generalization, specialization, by separating and collecting ideas in fortunate new ways, new and fruitful problems, and appears then itself as the real questioner. David Hilbert, Mathematical Problems Thestudyoflocallynipotentderivationsand G -actionshasrecentlyemerged a from the long shadows of other branches of mathematics, branches whose provenance is older and more distinguished. The subject grew out of the rich environment of Lie theory, invariant theory, and di?erential equations, and continues to draw inspiration from these and other ?elds. At the heart of the present exposition lie sixteen principles for locally nilpotent derivations, laid out in Chapter 1. These provide the foundation upon which the subsequent theory is built. As a rule, we would like to dist- guish which properties of a locally nilpotent derivation are due to its being a “derivation”, and which are special to the condition “locally nilpotent”. Thus, we ?rst consider general properties of derivations. The sixteen First Principles which follow can then be seen as belonging especially to the locally nilpotent derivations.