Algebraic theory of locally nilpotent derivations
Author(s)
Bibliographic Information
Algebraic theory of locally nilpotent derivations
（Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze, v. 136 . Invariant theory and algebraic transformation groups ; 7）
Springer, c2006
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
FRE||44||1||複本200003622334
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Note
Includes bibliographical references (p. [243]-256) and index
Description and Table of Contents
Description
This book explores the theory and application of locally nilpotent derivations. It provides a unified treatment of the subject, beginning with sixteen First Principles on which the entire theory is based. These are used to establish classical results, such as Rentschler's Theorem for the plane, right up to the most recent results, such as Makar-Limanov's Theorem for locally nilpotent derivations of polynomial rings. The book also includes a wealth of pexamples and open problems.
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.
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