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Symmetries, Lie Algebras and Representations, Fuchs/Schweigert



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Автор: Fuchs/Schweigert
Название:  Symmetries, Lie Algebras and Representations   (Симметрия, алгебра Ли и репрезентации)
Издательство: Cambridge Academ
Классификация:
Алгебра
ФИЗИКА

ISBN: 0521541190
ISBN-13(EAN): 9780521541190
ISBN: 0-521-54119-0
ISBN-13(EAN): 978-0-521-54119-0
Обложка/Формат: Paperback
Страницы: 464
Вес: 0.834 кг.
Дата издания: 07.10.2003
Серия: Cambridge monographs on mathematical physics
Язык: English
Издание: New ed
Иллюстрации: 36 line figures 18 tables 188 exercises
Размер: 246 x 192 x 25
Читательская аудитория: Professional & vocational
Подзаголовок: A graduate course for physicists
Ссылка на Издательство: Link
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Поставляется из: Англии
Описание: This is an introduction to Lie algebras and their applications in physics. The first three chapters show how Lie algebras arise naturally from symmetries of physical systems and illustrate through examples much of their general structure. Chapters 4 to 13 give a detailed introduction to Lie algebras and their representations, covering the Cartan-Weyl basis, simple and affine Lie algebras, real forms and Lie groups, the Weyl group, automorphisms, loop algebras and highest weight representations. Chapters 14 to 22 cover specific further topics, such as Verma modules, Casimirs, tensor products and Clebsch-Gordan coefficients, invariant tensors, subalgebras and branching rules, Young tableaux, spinors, Clifford algebras and supersymmetry, representations on function spaces, and Hopf algebras and representation rings. A detailed reference list is provided, and many exercises and examples throughout the book illustrate the use of Lie algebras in real physical problems. The text is written at a level accessible to graduate students, but will also provide a comprehensive reference for researchers.
Дополнительное описание: Subject: Physics / Theoretical Physics and Mathematical Physics
Readership: physics, theoretical physics, mathematics
Level: academic researchers, graduate students
Format: 460pp 36 line diagrams 18 tables 188 exercises
Chapter Titles: Preface; 1. Symmetries and conservation laws; 2. Basic examples; 3. The Lie algebra su(3) and hadron symmetries; 4. Formalization: algebras and Lie algebras; 5. Representations; 6. The Cartan-Weyl basis; 7. Simple and affine Lie algebras; 8. Real Lie algebras and real forms; 9. Lie groups; 10. Symmetries of the root system. The Weyl group; 11. Automorphisms of Lie algebras; 12. Loop algebras and central extensions; 13. Highest weight representations; 14. Verma modules, Casimirs, and the character formula; 15. Tensor products of representations; 16. Clebsch-Gordan coefficients and tensor operators; 17. Invariant tensors; 18. Subalgebras and branching rules; 19. Young tableaux and the symmetric group; 20. Spinors, Clifford algebras, and supersymmetry; 21. Representations on function spaces; 22. Hopf algebras and representation rings; Epilogue; References; Index.





Symmetries

Автор: Johnson D.L.
Название: Symmetries
ISBN: 1852332700 ISBN-13(EAN): 9781852332709
Издательство: Springer
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Цена: 3652 р.
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Описание: The main  object of study for this book is geometry, with group theory providing an appropriate language in which to express geometrical ideas.  Key features include: An overview of the preliminaries from group theory and geometry Coverage of the discrete subgroups of the Euclidean group A clear and complete derivation and classification of the 17 plane crystallographic groups Tessellations of various spaces (they are constructed, described and classified) A brief introduction to hyperbolic geometry.  Each chapter contains a number of exercises, most with solutions, and suggestions for background, alternative and further reading.  The author's accessible and down-to-earth approach make this an ideal introduction for readers in the second or third year of a mathematics undergraduate course.  It is also recommended for mechanical engineers, architects, physicists and crystallographers needing an understanding of 3-dimensional geometry, symmetry and trigonometry.

Complex Semisimple Lie Algebras

Автор: Serre Jean-Pierre, Jones G.A.
Название: Complex Semisimple Lie Algebras
ISBN: 3540678271 ISBN-13(EAN): 9783540678274
Издательство: Springer
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Цена: 5224 р.
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Описание: These notes, already well known in their original French edition, give the basic theory of semisimple Lie algebras over the complex numbers including the basic classification theorem. The author begins with a summary of the general properties of nilpotent, solvable, and semisimple Lie algebras. Subsequent chapters introduce Cartan subalgebras, root systems, and representation theory. The theory is illustrated by using the example of sln; in particular, the representation theory of sl2 is completely worked out. The last chapter discusses the connection between Lie algebras and Lie groups, and is intended to guide the reader towards further study.

Introduction to Lie Algebras and Representation Theory

Автор: Humphreys
Название: Introduction to Lie Algebras and Representation Theory
ISBN: 0387900535 ISBN-13(EAN): 9780387900537
Издательство: Springer
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Цена: 5533 р.
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Описание: Introduces the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. Here, a good knowledge of linear algebra is presupposed, as well as some acquaintance with the methods of abstract algebra.

Introduction to Lie Algebras

Автор: Erdmann
Название: Introduction to Lie Algebras
ISBN: 1846280400 ISBN-13(EAN): 9781846280405
Издательство: Springer
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Цена: 3652 р.
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Описание: Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. It also acts as a self-study guide for graduate students and researchers in mathematics and theoretical physics.

Mirror Geometry of Lie Algebras, Lie Groups and Homogeneous Spaces

Автор: Sabinin Lev V.
Название: Mirror Geometry of Lie Algebras, Lie Groups and Homogeneous Spaces
ISBN: 1402025440 ISBN-13(EAN): 9781402025440
Издательство: Springer
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Цена: 11494 р.
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Описание: Describes an original formalism based on mirror symmetries of Lie groups, Lie algebras and Homogeneous spaces. This book should is useful for researchers in Lie Groups, Lie Algebras, Differential Geometry and their applications, as well as for other postgraduate and advanced graduate students in mathematics.

Lie Groups, Lie Algebras, and Representations

Автор: Hall
Название: Lie Groups, Lie Algebras, and Representations
ISBN: 0387401229 ISBN-13(EAN): 9780387401225
Издательство: Springer
Рейтинг:
Цена: 4906 р.
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Описание: This book addresses Lie groups, Lie algebras, and representation theory. In order to keep the prerequisites to a minimum, the author restricts attention to matrix Lie groups and Lie algebras. This approach keeps the discussion concrete, allows the reader to get to the heart of the subject quickly, and covers all of the most interesting examples. The book also introduces the often-intimidating machinery of roots and the Weyl group in a gradual way, using examples and representation theory as motivation. The text is divided into two parts. The first covers Lie groups and Lie algebras and the relationship between them, along with basic representation theory. The second part covers the theory of semisimple Lie groups and Lie algebras, beginning with a detailed analysis of the representations of SU(3). The author illustrates the general theory with numerous images pertaining to Lie algebras of rank two and rank three, including images of root systems, lattices of dominant integral weights, and weight diagrams. This book is sure to become a standard textbook for graduate students in mathematics and physics with little or no prior exposure to Lie theory. Brian Hall is an Associate Professor of Mathematics at the University of Notre Dame.

Representations of Lie Algebras

Автор: Henderson
Название: Representations of Lie Algebras
ISBN: 1107653614 ISBN-13(EAN): 9781107653610
Издательство: Cambridge Academ
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Цена: 4945 р.
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Описание: This bold and refreshing approach to Lie algebras assumes only modest prerequisites (linear algebra up to the Jordan canonical form and a basic familiarity with groups and rings), yet it reaches a major result in representation theory: the highest-weight classification of irreducible modules of the general linear Lie algebra. The author's exposition is focused on this goal rather than aiming at the widest generality and emphasis is placed on explicit calculations with bases and matrices. The book begins with a motivating chapter explaining the context and relevance of Lie algebras and their representations and concludes with a guide to further reading. Numerous examples and exercises with full solutions are included. Based on the author's own introductory course on Lie algebras, this book has been thoroughly road-tested by advanced undergraduate and beginning graduate students and it is also suited to individual readers wanting an introduction to this important area of mathematics.

Algebras, rings and their representations - proceedings of the international conference on algebras, modules and rings

Название: Algebras, rings and their representations - proceedings of the international conference on algebras, modules and rings
ISBN: 9812565981 ISBN-13(EAN): 9789812565983
Издательство: World Scientific Publishing
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Цена: 17141 р.
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Описание: Surveying the most influential developments in the field, this proceedings reviews the latest research on algebras and their representations, commutative and non-commutative rings, modules, conformal algebras, and torsion theories. The volume collects stimulating discussions from world-renowned names including Tsit-Yuen Lam, Larry Levy, Barbara Osofsky, and Patrick Smith.

Representations of Finite-Dimensional Algebras

Автор: Gabriel
Название: Representations of Finite-Dimensional Algebras
ISBN: 3540629904 ISBN-13(EAN): 9783540629900
Издательство: Springer
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Цена: 12016 р.
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Описание: Attempts to take us up to the point where we can find our way in the original literature. This book presents some basic material and some insights of the theory. It includes proofs for statements which in the authors` opinions are elementary, those which help further understanding.

Representations of Hecke Algebras at Roots of Unity

Автор: Geck
Название: Representations of Hecke Algebras at Roots of Unity
ISBN: 0857297155 ISBN-13(EAN): 9780857297150
Издательство: Springer
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Цена: 11494 р.
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Описание: The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory of cells, the authors develop an analogue of James' (1970) characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general. Presenting a systematic and unified treatment of representations of Hecke algebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theory of affine Hecke algebras and Cherednik algebras. The main results of this book are obtained by an interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Ariki's theorem, the combinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods. This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of the field with an interest in Hecke algebras.

Representations of *-Algebras, Locally Compact Groups, and Banach

Автор: J. M.G. Fell
Название: Representations of *-Algebras, Locally Compact Groups, and Banach
ISBN: 0122527216 ISBN-13(EAN): 9780122527210
Издательство: Elsevier Science
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Цена: 5742 р.
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Описание: This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowle

Metamorphoses of Hamiltonian Systems with Symmetries

Автор: Efstathiou Konstantinos
Название: Metamorphoses of Hamiltonian Systems with Symmetries
ISBN: 354024316X ISBN-13(EAN): 9783540243168
Издательство: Springer
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Цена: 3652 р.
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Описание: Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems. The parametric nature of these examples leads naturally to the study of the major qualitative changes of such systems (metamorphoses) as the parameters are varied. The symmetries of these systems, discrete or continuous, exact or approximate, are used to simplify the problem through a number of mathematical tools and techniques like normalization and reduction. The book moves gradually from finding relative equilibria using symmetry, to the Hamiltonian Hopf bifurcation and its relation to monodromy and, finally, to generalizations of monodromy.


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