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Representations of Lie Algebras, Henderson



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Автор: Henderson
Название:  Representations of Lie Algebras
Издательство: Cambridge Academ
Классификация:
ISBN: 1107653614
ISBN-13(EAN): 9781107653610
Обложка/Формат: Paperback
Страницы: 168
Вес: 0.252 кг.
Дата издания: 16.08.2012
Серия: Australian mathematical society lecture series
Язык: English
Иллюстрации: Worked examples or exercises; 10 line drawings, unspecified
Размер: 152 x 227 x 9
Читательская аудитория: Tertiary education (us: college)
Ключевые слова: Mathematics,Algebra, MATHEMATICS / Algebra / General
Основная тема: Mathematics
Подзаголовок: An introduction through gl(n)
Ссылка на Издательство: Link
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Поставляется из: Англии
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 authors 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 authors 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.



Symmetries, Lie Algebras and Representations

Автор: Fuchs/Schweigert
Название: Symmetries, Lie Algebras and Representations
ISBN: 0521541190 ISBN-13(EAN): 9780521541190
Издательство: Cambridge Academ
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Цена: 7821 р.
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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.

Algebraic Integrability, PainlevГ© Geometry and Lie Algebras

Автор: Adler Mark, Moerbeke Pierre van, Vanhaecke Pol
Название: Algebraic Integrability, PainlevГ© Geometry and Lie Algebras
ISBN: 354022470X ISBN-13(EAN): 9783540224709
Издательство: Springer
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Цена: 14629 р.
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Описание: 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 PainlevГ© 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.

Lie Groups, Lie Algebras, and Representations

Автор: Hall
Название: Lie Groups, Lie Algebras, and Representations
ISBN: 0387401229 ISBN-13(EAN): 9780387401225
Издательство: Springer
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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.

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

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.

Elements of Mathematics. Lie Groups and Lie Algebras / Chapters 4-6

Автор: Bourbaki Nicolas, Pressley A.
Название: Elements of Mathematics. Lie Groups and Lie Algebras / Chapters 4-6
ISBN: 3540426507 ISBN-13(EAN): 9783540426509
Издательство: Springer
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Цена: 10445 р.
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Описание: From the reviews of the French edition: "This is a rich and useful volume. The material it treats has relevance well beyond the theory of Lie groups and algebras, ranging from the geometry of regular polytopes and paving problems to current work on finite simple groups having a (B,N)-pair structure, or "Tits systems". A historical note provides a survey of the contexts in which groups generated by reflections have arisen. A brief introduction includes almost the only other mention of Lie groups and algebras to be found in the volume. Thus the presentation here is really quite independent of Lie theory. The choice of such an approach makes for an elegant, self-contained treatment of some highly interesting mathematics, which can be read with profit and with relative ease by a very wide circle of readers (and with delight by many, if the reviewer is at all representative)."(G.B. Seligman in MathReviews)

Lie Algebras and Lie Groups / 1964 Lectures given at Harvard University

Автор: Serre Jean-Pierre
Название: Lie Algebras and Lie Groups / 1964 Lectures given at Harvard University
ISBN: 3540550089 ISBN-13(EAN): 9783540550082
Издательство: Springer
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Цена: 3652 р.
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Описание: This book reproduces J-P. Serre's 1964 Harvard lectures. The aim is to introduce the reader to the "Lie dictionary": Lie algebras and Lie groups. Special features of the presentation are its emphasis on formal groups (in the Lie group part) and the use of analytic manifolds on p-adic fields. Some knowledge of algebra and calculus is required of the reader, but the text is easily accessible to graduate students, and to mathematicians at large.

Elements of Mathematics / Lie Groups and Lie Algebras: Chapters 7-9

Автор: Bourbaki Nicolas, Pressley A.N.
Название: Elements of Mathematics / Lie Groups and Lie Algebras: Chapters 7-9
ISBN: 3540434054 ISBN-13(EAN): 9783540434054
Издательство: Springer
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Цена: 10445 р.
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Описание: This is the English translation of Bourbaki's text Groupes et AlgГЁbres de Lie, Chapters 7 to 9. It completes the previously published translations of Chapters 1 to 3 (3-540-64242-0) and 4 to 6 (3-540-42650-7) by covering the structure and representation theory of semi-simple Lie algebras and compact Lie groups. Chapter 7 deals with Cartan subalgebras of Lie algebras, regular elements and conjugacy theorems. Chapter 8 begins with the structure of split semi-simple Lie algebras and their root systems. It goes on to describe the finite-dimensional modules for such algebras, including the character formula of Hermann Weyl. It concludes with the theory of Chevalley orders. Chapter 9 is devoted to the theory of compact Lie groups, beginning with a discussion of their maximal tori, root systems and Weyl groups. It goes on to describe the representation theory of compact Lie groups, including the application of integration to establish Weyl's formula in this context. The chapter concludes with a discussion of the actions of compact Lie groups on manifolds. The nine chapters together form the most comprehensive text available on the theory of Lie groups and Lie algebras.

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.


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