Algebraic Theory of Locally Nilpotent Derivations - Gene Freudenburg

Algebraic Theory of Locally Nilpotent Derivations

Buch | Softcover
XXII, 319 Seiten
2018 | 2. Softcover reprint of the original 2nd ed. 2017
Springer Berlin (Verlag)
978-3-662-57230-6 (ISBN)
160,49 inkl. MwSt
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.

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.

Erscheinungsdatum
Reihe/Serie Encyclopaedia of Mathematical Sciences
Zusatzinfo XXII, 319 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 5212 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Geometrie / Topologie
Schlagworte additive group action on affine varieties • Algebra • Algebraic Geometry • Commutative algebra • Dimension • Invariant theory
ISBN-10 3-662-57230-3 / 3662572303
ISBN-13 978-3-662-57230-6 / 9783662572306
Zustand Neuware
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