Algebraic Theory of Locally Nilpotent Derivations

This book explores the theory and application of locally nilpotent derivations, which is a subject of growing interest and importance not only among those in commutative algebra and algebraic geometry, but also in fields such as Lie algebras and differential equations. The author provides a unified...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Freudenburg, Gene (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2006.
Edición:1st ed. 2006.
Colección:Encyclopaedia of Mathematical Sciences ; 136
Temas:
Commutative algebra.
Commutative rings.
Algebraic geometry.
Topological groups.
Lie groups.
Commutative Rings and Algebras.
Algebraic Geometry.
Topological Groups and Lie Groups.
Acceso en línea:Texto Completo

MARC

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245 1 0 |a Algebraic Theory of Locally Nilpotent Derivations  |h [electronic resource] /  |c by Gene Freudenburg. 
246 3 |a Invariant Theory and Algebraic Transformation Groups VII 
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264 1 |a Berlin, Heidelberg :  |b Springer Berlin Heidelberg :  |b Imprint: Springer,  |c 2006. 
300 |a XI, 261 p.  |b online resource. 
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490 1 |a Encyclopaedia of Mathematical Sciences ;  |v 136 
505 0 |a First Principles -- Further Properties of Locally Nilpotent Derivations -- Polynomial Rings -- Dimension Two -- Dimension Three -- Linear Actions of Unipotent Groups -- Non-Finitely Generated Kernels -- Algorithms -- The Makar-Limanov and Derksen Invariants -- Slices, Embeddings and Cancellation -- Epilogue. 
520 |a This book explores the theory and application of locally nilpotent derivations, which is a subject of growing interest and importance not only among those in commutative algebra and algebraic geometry, but also in fields such as Lie algebras and differential equations. The author provides a unified treatment of the subject, beginning with 16 First Principles on which the entire theory is based. These are used to establish classical results, such as Rentschler's Theorem for the plane, right up to the most recent results, such as Makar-Limanov's Theorem for locally nilpotent derivations of polynomial rings. Topics of special interest include: progress in the dimension three case, finiteness questions (Hilbert's 14th Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem. The reader will also find a wealth of pertinent examples and open problems and an up-to-date resource for research. . 
650 0 |a Commutative algebra. 
650 0 |a Commutative rings. 
650 0 |a Algebraic geometry. 
650 0 |a Topological groups. 
650 0 |a Lie groups. 
650 1 4 |a Commutative Rings and Algebras. 
650 2 4 |a Algebraic Geometry. 
650 2 4 |a Topological Groups and Lie Groups. 
710 2 |a SpringerLink (Online service) 
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776 0 8 |i Printed edition:  |z 9783642067327 
776 0 8 |i Printed edition:  |z 9783540816942 
776 0 8 |i Printed edition:  |z 9783540295211 
830 0 |a Encyclopaedia of Mathematical Sciences ;  |v 136 
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950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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