Algebraic Theory of Locally Nilpotent Derivations: Encyclopaedia of Mathematical Sciences, cartea 136
Autor Gene Freudenburgen Limba Engleză Hardback – 18 sep 2017
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.
Toate formatele și edițiile | Preț | Express |
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Paperback (2) | 865.82 lei 6-8 săpt. | |
Springer Berlin, Heidelberg – 16 noi 2010 | 865.82 lei 6-8 săpt. | |
Springer Berlin, Heidelberg – 18 mai 2018 | 927.55 lei 6-8 săpt. | |
Hardback (1) | 933.59 lei 6-8 săpt. | |
Springer Berlin, Heidelberg – 18 sep 2017 | 933.59 lei 6-8 săpt. |
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Specificații
ISBN-13: 9783662553480
ISBN-10: 3662553481
Pagini: 319
Ilustrații: XXII, 319 p.
Dimensiuni: 155 x 235 x 28 mm
Greutate: 0.66 kg
Ediția:2nd ed. 2017
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Encyclopaedia of Mathematical Sciences
Locul publicării:Berlin, Heidelberg, Germany
ISBN-10: 3662553481
Pagini: 319
Ilustrații: XXII, 319 p.
Dimensiuni: 155 x 235 x 28 mm
Greutate: 0.66 kg
Ediția:2nd ed. 2017
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Encyclopaedia of Mathematical Sciences
Locul publicării:Berlin, Heidelberg, Germany
Cuprins
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.
Textul de pe ultima copertă
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.
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.
Caracteristici
2nd enlarged edition of first monograph on this topic Lot of new material Wealth of examples and open problems Includes supplementary material: sn.pub/extras
Recenzii
From the reviews:
"In the volume under review, the author gives a detailed description of the subject covering all the important results … . the book has a wealth of examples and the Epilogue details some important open problems in the area. … is accessible to less advanced graduate students. It is a valuable addition to the literature and am sure would be very helpful to the interested student and researcher alike." (N. Mohan Kumar, Zentralblatt MATH, Vol. 1121 (23), 2007)
"In the volume under review, the author gives a detailed description of the subject covering all the important results … . the book has a wealth of examples and the Epilogue details some important open problems in the area. … is accessible to less advanced graduate students. It is a valuable addition to the literature and am sure would be very helpful to the interested student and researcher alike." (N. Mohan Kumar, Zentralblatt MATH, Vol. 1121 (23), 2007)