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Encyclopaedia of Mathematical Sciences Ser.: Algebraic Theory of Locally Nilpotent Derivations by Gene Freudenburg (2017, Hardcover)

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About this product

Product Identifiers

PublisherSpringer Berlin / Heidelberg

ISBN-103662553481

ISBN-139783662553480

eBay Product ID (ePID)237789651

Product Key Features

Number of PagesXxii, 319 Pages

Publication NameAlgebraic Theory of Locally Nilpotent Derivations

LanguageEnglish

Publication Year2017

SubjectGroup Theory, Algebra / Abstract, Algebra / General, Geometry / Algebraic

TypeTextbook

AuthorGene Freudenburg

Subject AreaMathematics

SeriesEncyclopaedia of Mathematical Sciences Ser.

FormatHardcover

Dimensions

Item Weight225.3 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Edition Number2

Series Volume Number136

Number of Volumes1 vol.

IllustratedYes

Table Of ContentIntroduction.- 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.

SynopsisThis 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.

LC Classification NumberQA251.3