Overview
- 2nd enlarged edition of first monograph on this topic
- Lot of new material
- Wealth of examples and open problems
- Includes supplementary material: sn.pub/extras
Part of the book series: Encyclopaedia of Mathematical Sciences (EMS, volume 136.3)
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Table of contents (11 chapters)
Keywords
About this book
This book explores the theory and application of locally nilpotent derivations, a subject motivated by questions in affine algebraic geometry and having fundamental connections to areas such as commutative algebra, representation theory, Lie algebras and differential equations.
The author provides a unified treatment of the subject, beginning with 16 First Principles on which the theory is based. These are used to establish classical results, such as Rentschler's Theorem for the plane and the Cancellation Theorem for Curves.
More recent results, such as Makar-Limanov's theorem for locally nilpotent derivations of polynomial rings, are also discussed. Topics of special interest include progress in classifying additive actions on three-dimensional affine space, finiteness questions (Hilbert's 14th Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem.
A lot of new material is included in this expanded second edition, such as canonical factorization of quotient morphisms, and a more extended treatment of linear actions. The reader will also find a wealth of examples and open problems and an updated resource for future investigations.
Authors and Affiliations
Bibliographic Information
Book Title: Algebraic Theory of Locally Nilpotent Derivations
Authors: Gene Freudenburg
Series Title: Encyclopaedia of Mathematical Sciences
DOI: https://doi.org/10.1007/978-3-662-55350-3
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag GmbH Germany 2017
Hardcover ISBN: 978-3-662-55348-0Published: 18 September 2017
Softcover ISBN: 978-3-662-57230-6Published: 18 May 2018
eBook ISBN: 978-3-662-55350-3Published: 08 September 2017
Series ISSN: 0938-0396
Edition Number: 2
Number of Pages: XXII, 319
Topics: Commutative Rings and Algebras, Algebraic Geometry, Topological Groups, Lie Groups