Skip to main content
SpringerLink
Log in

Algebraic Theory of Locally Nilpotent Derivations

  • Book
  • © 2006

Overview

Authors:
  1. Gene Freudenburg

    1. Department of Mathematics, Western Michigan University, Kalamazoo, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • First monograph on topic

Part of the book series: Encyclopaedia of Mathematical Sciences (EMS, volume 136)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 119.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 159.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (12 chapters)

  1. Front Matter

    Pages I-XI
    Download chapter PDF

  2. Introduction

    • Gene Freudenburg
    Pages 1-7

  3. First Principles

    • Gene Freudenburg
    Pages 9-33

  4. Further Properties of Locally Nilpotent Derivations

    • Gene Freudenburg
    Pages 35-47

  5. Polynomial Rings

    • Gene Freudenburg
    Pages 49-82

  6. Dimension Two

    • Gene Freudenburg
    Pages 83-106

  7. Dimension Three

    • Gene Freudenburg
    Pages 107-136

  8. Linear Actions of Unipotent Groups

    • Gene Freudenburg
    Pages 137-156

  9. Non-Finitely Generated Kernels

    • Gene Freudenburg
    Pages 157-180

  10. Algorithms

    • Gene Freudenburg
    Pages 181-194

  11. The Makar-Limanov and Derksen Invariants

    • Gene Freudenburg
    Pages 195-217

  12. Slices, Embeddings and Cancellation

    • Gene Freudenburg
    Pages 219-234

  13. Epilogue

    • Gene Freudenburg
    Pages 235-242

  14. Back Matter

    Pages 243-261
    Download chapter PDF
Back to top

Keywords

About this book

This book explores the theory and application of locally nilpotent derivations, which is a subject of growing interest and importance not only among those in commutative algebra and algebraic geometry, but also in fields such as Lie algebras and differential equations. 


The author provides a unified treatment of the subject, beginning with 16 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. Topics of special interest include: progress in the dimension three case, finiteness questions (Hilbert’s 14th Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem. The reader will also find a wealth of pertinent examples and open problems and an up-to-date resource for research.

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)

Authors and Affiliations

  • Department of Mathematics, Western Michigan University, Kalamazoo, USA

    Gene Freudenburg

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation