Algebraic Theory of Locally Nilpotent Derivations. 2nd ed. 2017

種類:

電子ブック

責任表示:

by Gene Freudenburg

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2017

著者名:

• Freudenburg, Gene.
• SpringerLink (Online service)

シリーズ名:

Encyclopaedia of Mathematical Sciences ; 136.3

ISBN:

9783662553503 [3662553503]    

注記:

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 factorizat

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