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Encyclopaedia of Mathematical Sciences Invariant Theory and Algebraic Transformation Groups

Algebraic Theory of Locally Nilpotent Derivations

Authors: Freudenburg, Gene

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  • 2nd enlarged edition of first monograph on this topic
  • Lot of new material
  • Wealth of examples and open problems
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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.

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook 106,99 €
price for Spain (gross)
  • ISBN 978-3-662-55350-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 135,19 €
price for Spain (gross)
  • ISBN 978-3-662-55348-0
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 135,19 €
price for Spain (gross)
  • ISBN 978-3-662-57230-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic Theory of Locally Nilpotent Derivations
Authors
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
136
Copyright
2017
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag GmbH Germany
eBook ISBN
978-3-662-55350-3
DOI
10.1007/978-3-662-55350-3
Hardcover ISBN
978-3-662-55348-0
Softcover ISBN
978-3-662-57230-6
Series ISSN
0938-0396
Edition Number
2
Number of Pages
XXII, 319
Topics

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