Algebraic Integrability, Painlevé Geometry and Lie Algebras PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Algebraic Integrability, Painlevé Geometry and Lie Algebras PDF full book. Access full book title Algebraic Integrability, Painlevé Geometry and Lie Algebras by Mark Adler. Download full books in PDF and EPUB format.
Author: Mark Adler
Publisher: Springer Science & Business Media
ISBN: 366205650X
Category : Mathematics
Languages : en
Pages : 487
Get Book
Book Description
This Ergebnisse volume is aimed at a wide readership of mathematicians and physicists, graduate students and professionals. The main thrust of the book is to show how algebraic geometry, Lie theory and Painlevé analysis can be used to explicitly solve integrable differential equations and construct the algebraic tori on which they linearize; at the same time, it is, for the student, a playing ground to applying algebraic geometry and Lie theory. The book is meant to be reasonably self-contained and presents numerous examples. The latter appear throughout the text to illustrate the ideas, and make up the core of the last part of the book. The first part of the book contains the basic tools from Lie groups, algebraic and differential geometry to understand the main topic.
Author: Mark Adler
Publisher: Springer Science & Business Media
ISBN: 366205650X
Category : Mathematics
Languages : en
Pages : 487
Get Book
Book Description
This Ergebnisse volume is aimed at a wide readership of mathematicians and physicists, graduate students and professionals. The main thrust of the book is to show how algebraic geometry, Lie theory and Painlevé analysis can be used to explicitly solve integrable differential equations and construct the algebraic tori on which they linearize; at the same time, it is, for the student, a playing ground to applying algebraic geometry and Lie theory. The book is meant to be reasonably self-contained and presents numerous examples. The latter appear throughout the text to illustrate the ideas, and make up the core of the last part of the book. The first part of the book contains the basic tools from Lie groups, algebraic and differential geometry to understand the main topic.
Author: Mark Adler
Publisher: Springer
ISBN: 9783662056516
Category :
Languages : en
Pages : 502
Get Book
Book Description
Author: A.T. Fomenko
Publisher: Springer Science & Business Media
ISBN: 9789027728180
Category : Mathematics
Languages : en
Pages : 370
Get Book
Book Description
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. 1hen one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin' . • 1111 Oulik'. n. . Chi" •. • ~ Mm~ Mu,d. ", Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Author: Alexander Vitalievich Razumov
Publisher: Cambridge University Press
ISBN: 0521479231
Category : Mathematics
Languages : en
Pages : 271
Get Book
Book Description
The book describes integrable Toda type systems and their Lie algebra and differential geometry background.
Author: Ron Donagi
Publisher: Cambridge University Press
ISBN: 110880358X
Category : Mathematics
Languages : en
Pages : 421
Get Book
Book Description
Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. This first volume covers a wide range of areas related to integrable systems, often emphasizing the deep connections with algebraic geometry. Common themes include theta functions and Abelian varieties, Lax equations, integrable hierarchies, Hamiltonian flows and difference operators. These powerful tools are applied to spinning top, Hitchin, Painleve and many other notable special equations.
Author: Lionel Mason
Publisher: Cambridge University Press
ISBN: 9780521529990
Category : Mathematics
Languages : en
Pages : 170
Get Book
Book Description
Articles from leading researchers to introduce the reader to cutting-edge topics in integrable systems theory.
Author: Amit K. Roy-Chowdhury
Publisher: CRC Press
ISBN: 1000116786
Category : Mathematics
Languages : en
Pages : 367
Get Book
Book Description
Over the last thirty years, the subject of nonlinear integrable systems has grown into a full-fledged research topic. In the last decade, Lie algebraic methods have grown in importance to various fields of theoretical research and worked to establish close relations between apparently unrelated systems. The various ideas associated with Lie algebra and Lie groups can be used to form a particularly elegant approach to the properties of nonlinear systems. In this volume, the author exposes the basic techniques of using Lie algebraic concepts to explore the domain of nonlinear integrable systems. His emphasis is not on developing a rigorous mathematical basis, but on using Lie algebraic methods as an effective tool. The book begins by establishing a practical basis in Lie algebra, including discussions of structure Lie, loop, and Virasor groups, quantum tori and Kac-Moody algebras, and gradation. It then offers a detailed discussion of prolongation structure and its representation theory, the orbit approach-for both finite and infinite dimension Lie algebra. The author also presents the modern approach to symmetries of integrable systems, including important new ideas in symmetry analysis, such as gauge transformations, and the "soldering" approach. He then moves to Hamiltonian structure, where he presents the Drinfeld-Sokolov approach, the Lie algebraic approach, Kupershmidt's approach, Hamiltonian reductions and the Gelfand Dikii formula. He concludes his treatment of Lie algebraic methods with a discussion of the classical r-matrix, its use, and its relations to double Lie algebra and the KP equation.
Author: Pol Vanhaecke
Publisher: Springer Verlag
ISBN:
Category : Mathematics
Languages : en
Pages : 240
Get Book
Book Description
2. Divisors and line bundles 97 2.1. Divisors . . 97 2.2. Line bundles 98 2.3. Sections of line bundles 99 2.4. The Riemann-Roch Theorem 101 2.5. Line bundles and embeddings in projective space 103 2.6. Hyperelliptic curves 104 3. Abelian varieties 106 3.1. Complex tori and Abelian varieties 106 3.2. Line bundles on Abelian varieties 107 3.3. Abelian surfaces 109 4. Jacobi varieties . . . 112 4.1. The algebraic Jacobian 112 4.2. The analytic/trancendental Jacobian 112 4.3. Abel's Theorem and Jacobi inversion 116 4.4. Jacobi and Kummer surfaces 118 4.5. Abelian surfaces of type (1.4) 120 V. Algebraic completely integrable Hamiltonian systems 123 1. Introduction . 123 2. A.c.i. systems 125 3. Painleve analysis for a.c.i. systems 131 4. Linearization of two-dimensional a.c.i. systems 134 5. Lax equations 136 VI. The master systems 139 1. Introduction . . . . .
Author: Ivan Penkov
Publisher: Springer Nature
ISBN: 3030896609
Category : Mathematics
Languages : en
Pages : 245
Get Book
Book Description
Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
Author: Anthony W. Knapp
Publisher: Princeton University Press
ISBN: 069108498X
Category : Mathematics
Languages : en
Pages : 522
Get Book
Book Description
This book starts with the elementary theory of Lie groups of matrices and arrives at the definition, elementary properties, and first applications of cohomological induction, which is a recently discovered algebraic construction of group representations. Along the way it develops the computational techniques that are so important in handling Lie groups. The book is based on a one-semester course given at the State University of New York, Stony Brook in fall, 1986 to an audience having little or no background in Lie groups but interested in seeing connections among algebra, geometry, and Lie theory. These notes develop what is needed beyond a first graduate course in algebra in order to appreciate cohomological induction and to see its first consequences. Along the way one is able to study homological algebra with a significant application in mind; consequently one sees just what results in that subject are fundamental and what results are minor.
