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Lie Groups, Lie Algebras, and Their Representation, Varadarajan



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Автор: Varadarajan
Название:  Lie Groups, Lie Algebras, and Their Representation
ISBN: 9780387909691
Издательство: Springer
Классификация:
ISBN-10: 0387909699
Обложка/Формат: Hardback
Страницы: 465
Вес: 0.807 кг.
Дата издания: 01/06/1984
Серия: Topological Groups, Lie Groups / Graduate Texts in Mathematics
Язык: English
Иллюстрации: Black & white illustrations
Размер: 23.39 x 15.60 x 2.54
Читательская аудитория: Professional & VocationalPostgraduate, Research &
Ссылка на Издательство: Link
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Поставляется из: Германии



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Introduction to Lie Algebras and Representation Theory

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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.

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Complex Semisimple Lie Algebras

Автор: Serre Jean-Pierre, Jones G.A.
Название: Complex Semisimple Lie Algebras
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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 the Representation Theory of Associative Algebras

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Описание: The second of a three-volume set providing a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The subject is presented from the perspective of linear representations of quivers, geometry of tubes of indecomposable modules, and homological algebra. This volume provides an up-to-date introduction to the representation theory of the representation-infinite hereditary algebras of Euclidean type, as well as to concealed algebras of Euclidean type. The book is primarily addressed to a graduate student starting research in the representation theory of algebras, but it will also be of interest to mathematicians in other fields. The text includes many illustrative examples and a large number of exercises at the end of each of the chapters. Proofs are presented in complete detail, making the book suitable for courses, seminars, and self-study.

Elements of the Representation Theory of Associative Algebras

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Описание: Provides an elementary but up-to-date introduction to the representation theory of algebras.

Elements of the Representation Theory of Associative Algebras

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Описание: The final part of a three-volume set providing a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The subject is presented from the perspective of linear representations of quivers and homological algebra. This volume provides an introduction to the representation theory of representation-infinite tilted algebras from the point of view of the time-wild dichotomy. Also included is a collection of selected results relating to the material discussed in all three volumes. The book is primarily addressed to a graduate student starting research in the representation theory of algebras, but will also be of interest to mathematicians in other fields. Proofs are presented in complete detail, and the text includes many illustrative examples and a large number of exercises at the end of each chapter, making the book suitable for courses, seminars, and self-study.

Schur Algebras and Representation Theory

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Описание: This is the first comprehensive text in this important and active area of research.

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

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Издательство: Springer
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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)

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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.

Lie Groups, Lie Algebras, and Representations

Автор: Hall
Название: Lie Groups, Lie Algebras, and Representations
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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.


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