Algebraic Theory of Locally Nilpotent Derivations by Gene FreudenburgAlgebraic Theory of Locally Nilpotent Derivations by Gene Freudenburg

Algebraic Theory of Locally Nilpotent Derivations

byGene Freudenburg

Paperback | November 16, 2010

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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.
Title:Algebraic Theory of Locally Nilpotent DerivationsFormat:PaperbackDimensions:261 pagesPublished:November 16, 2010Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3642067328

ISBN - 13:9783642067327


Table of Contents

First Principles.- Further Properties of Locally Nilpotent Derivations.- Polynomial Rings.- Dimension Two.- Dimension Three.- Linear Actions of Unipotent Groups.- Non-Finitely Generated Kernels.- Algorithms.- The Makar-Limanov and Derksen Invariants.- Slices, Embeddings and Cancellation.- Epilogue.

Editorial Reviews

From the reviews:"In the volume under review, the author gives a detailed description of the subject covering all the important results . . the book has a wealth of examples and the Epilogue details some important open problems in the area. . is accessible to less advanced graduate students. It is a valuable addition to the literature and am sure would be very helpful to the interested student and researcher alike." (N. Mohan Kumar, Zentralblatt MATH, Vol. 1121 (23), 2007)