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Algebraic theory of locally nilpoten...

Freudenburg, Gene.

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Algebraic theory of locally nilpotent derivations

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Algebraic theory of locally nilpotent derivations/ by Gene Freudenburg.
作者:	Freudenburg, Gene.
出版者:	Berlin, Heidelberg :Springer Berlin Heidelberg : : 2017.,
面頁冊數:	xxii, 319 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer eBooks
標題:	Geometry, Algebraic. -
電子資源:	http://dx.doi.org/10.1007/978-3-662-55350-3
ISBN:	9783662553503

Algebraic theory of locally nilpotent derivations
Freudenburg, Gene.

Algebraic theory of locally nilpotent derivations[electronic resource] /by Gene Freudenburg. - 2nd ed. - Berlin, Heidelberg :Springer Berlin Heidelberg :2017. - xxii, 319 p. :ill., digital ;24 cm. - Encyclopaedia of mathematical sciences,v.1360938-0396 ;. - Encyclopaedia of mathematical sciences ;v.136..

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 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.

ISBN: 9783662553503

Standard No.: 10.1007/978-3-662-55350-3doiSubjects--Topical Terms:

532048
Geometry, Algebraic.

LC Class. No.: QA564 / .F75 2017

Dewey Class. No.: 516.35

Algebraic theory of locally nilpotent derivations
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520 $a 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.
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