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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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Bibliographic Details
Main Author: Freudenburg, Gene
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2006, 2006
Edition:1st ed. 2006
Series:Encyclopaedia of Mathematical Sciences
Subjects:
Commutative Algebra
Algebraic Geometry
Commutative Rings And Algebras
Topological Groups And Lie Groups
Lie Groups
Topological Groups
Commutative Rings
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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245 0 0 |a Algebraic Theory of Locally Nilpotent Derivations  |h Elektronische Ressource  |c by Gene Freudenburg 
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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 
653 |a Commutative algebra 
653 |a Algebraic Geometry 
653 |a Commutative Rings and Algebras 
653 |a Topological Groups and Lie Groups 
653 |a Lie groups 
653 |a Topological groups 
653 |a Commutative rings 
653 |a Algebraic geometry 
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490 0 |a Encyclopaedia of Mathematical Sciences 
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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. 

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