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| Author | : Alexander Vitalievich Razumov |
| Publisher | : Cambridge University Press |
| Total Pages | : 271 |
| Release | : 1997-05-15 |
| Genre | : Mathematics |
| ISBN | : 0521479231 |
The book describes integrable Toda type systems and their Lie algebra and differential geometry background.
| Author | : R Costa |
| Publisher | : CRC Press |
| Total Pages | : 492 |
| Release | : 2019-05-20 |
| Genre | : Mathematics |
| ISBN | : 0429529996 |
A collection of lectures presented at the Fourth International Conference on Nonassociative Algebra and its Applications, held in Sao Paulo, Brazil. Topics in algebra theory include alternative, Bernstein, Jordan, lie, and Malcev algebras and superalgebras. The volume presents applications to population genetics theory, physics, and more.
| Author | : Fritz Gesztesy |
| Publisher | : Cambridge University Press |
| Total Pages | : 438 |
| Release | : 2008-09-04 |
| Genre | : Mathematics |
| ISBN | : 1139473778 |
As a partner to Volume 1: Dimensional Continuous Models, this monograph provides a self-contained introduction to algebro-geometric solutions of completely integrable, nonlinear, partial differential-difference equations, also known as soliton equations. The systems studied in this volume include the Toda lattice hierarchy, the Kac-van Moerbeke hierarchy, and the Ablowitz-Ladik hierarchy. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The theory presented includes trace formulas, algebro-geometric initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses basic techniques from the theory of difference equations and spectral analysis, some elements of algebraic geometry and especially, the theory of compact Riemann surfaces. The presentation is constructive and rigorous, with ample background material provided in various appendices. Detailed notes for each chapter, together with an exhaustive bibliography, enhance understanding of the main results.
| Author | : A V Gladyshev |
| Publisher | : World Scientific |
| Total Pages | : 479 |
| Release | : 2002-03-28 |
| Genre | : Science |
| ISBN | : 981448962X |
This book addresses the theoretical, phenomenological and experimental aspects of supersymmetry in particle physics as well as its implications in cosmology.
| Author | : Erhard Neher |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 226 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 082185237X |
Lie theory has connections to many other disciplines such as geometry, number theory, mathematical physics, and algebraic combinatorics. The interaction between algebra, geometry and combinatorics has proven to be extremely powerful in shedding new light on each of these areas. This book presents the lectures given at the Fields Institute Summer School on Geometric Representation Theory and Extended Affine Lie Algebras held at the University of Ottawa in 2009. It provides a systematic account by experts of some of the exciting developments in Lie algebras and representation theory in the last two decades. It includes topics such as geometric realizations of irreducible representations in three different approaches, combinatorics and geometry of canonical and crystal bases, finite $W$-algebras arising as the quantization of the transversal slice to a nilpotent orbit, structure theory of extended affine Lie algebras, and representation theory of affine Lie algebras at level zero. This book will be of interest to mathematicians working in Lie algebras and to graduate students interested in learning the basic ideas of some very active research directions. The extensive references in the book will be helpful to guide non-experts to the original sources.
| Author | : D. I. Kazakov |
| Publisher | : World Scientific |
| Total Pages | : 488 |
| Release | : 2002 |
| Genre | : Science |
| ISBN | : 9789810248055 |
This book addresses the theoretical, phenomenological and experimental aspects of supersymmetry in particle physics as well as its implications in cosmology.
| Author | : Mark Adler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 487 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 366205650X |
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 | : V.I. Arnol'd |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 342 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 3662067919 |
From the reviews of the first edition:"... Here ... a wealth of material is displayed for us, too much to even indicate in a review. ... Your reviewer was very impressed by the contents of both volumes (EMS 2 and 4), recommending them without any restriction." Mededelingen van het Wiskundig genootshap 1992
| Author | : Patrice Tauvel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 650 |
| Release | : 2005-08-08 |
| Genre | : Mathematics |
| ISBN | : 3540274278 |
Devoted to the theory of Lie algebras and algebraic groups, this book includes a large amount of commutative algebra and algebraic geometry so as to make it as self-contained as possible. The aim of the book is to assemble in a single volume the algebraic aspects of the theory, so as to present the foundations of the theory in characteristic zero. Detailed proofs are included, and some recent results are discussed in the final chapters.
| Author | : Martin A. Guest |
| Publisher | : Cambridge University Press |
| Total Pages | : 202 |
| Release | : 1997-01-13 |
| Genre | : Mathematics |
| ISBN | : 9780521589321 |
Harmonic maps are generalisations of the concept of geodesics. They encompass many fundamental examples in differential geometry and have recently become of widespread use in many areas of mathematics and mathematical physics. This is an accessible introduction to some of the fundamental connections between differential geometry, Lie groups, and integrable Hamiltonian systems. The specific goal of the book is to show how the theory of loop groups can be used to study harmonic maps. By concentrating on the main ideas and examples, the author leads up to topics of current research. The book is suitable for students who are beginning to study manifolds and Lie groups, and should be of interest both to mathematicians and to theoretical physicists.
