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Algebraic Theory of Locally Nilpotent Derivations

  • Fester Einband
  • 319 Seiten
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Invariant Theory and Algebraic Transformation Groups VIIThis book explores the theory and application of locally nilpotent derivat... Weiterlesen
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Beschreibung

Invariant Theory and Algebraic Transformation Groups VII

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.



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


Inhalt
Introduction.- 1 First Principles.- 2 Further Properties of LNDs.- 3 Polynomial Rings.- 4 Dimension Two.- 5 Dimension Three.- 6 Linear Actions of Unipotent Groups.- 7 Non-Finitely Generated Kernels.- 8 Algorithms.- 9 Makar-Limanov and Derksen Invariants.- 10 Slices, Embeddings and Cancellation.- 11 Epilogue.- References.- Index.

Produktinformationen

Titel: Algebraic Theory of Locally Nilpotent Derivations
Untertitel: Encyclopaedia of Mathematical Sciences 136
Autor:
EAN: 9783662553480
ISBN: 978-3-662-55348-0
Format: Fester Einband
Herausgeber: Springer, Berlin
Genre: Mathematik
Anzahl Seiten: 319
Gewicht: 648g
Größe: H22mm x B244mm x T156mm
Jahr: 2017
Auflage: 2. Aufl.
Land: DE

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