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＜E-Book＞
Algebraic Theory of Locally Nilpotent Derivations / by Gene Freudenburg
(Encyclopaedia of Mathematical Sciences ; 136.3)

Edition	2nd ed. 2017.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2017
Language	English
Size	XXII, 319 p : online resource
Authors	*Freudenburg, Gene author SpringerLink (Online service)
Subjects	LCSH:Commutative algebra LCSH:Commutative rings LCSH:Algebraic geometry LCSH:Topological groups LCSH:Lie groups FREE:Commutative Rings and Algebras FREE:Algebraic Geometry FREE:Topological Groups and Lie Groups
Notes	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 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 includedin 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 HTTP:URL=https://doi.org/10.1007/978-3-662-55350-3

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