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Lie Groups Lie Algebras And Representations

Author: Brian Hall
Publisher: Springer
ISBN: 3319134671
Size: 55.87 MB
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This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended. — The Mathematical Gazette

Lie Groups Lie Algebras And Representations

Author: Brian Hall
Publisher: Springer Science & Business Media
ISBN: 9780387401225
Size: 28.77 MB
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This book addresses Lie groups, Lie algebras, and representation theory. 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.From the reviews:"Sure to become a standard textbook for graduate students in mathematics and physics with little or no prior exposure to Lie theory." --L'Enseignement Mathematique

Reelle Und Komplexe Analysis

Author: Walter Rudin
Publisher: Walter de Gruyter
ISBN: 9783486591866
Size: 24.98 MB
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Besonderen Wert legt Rudin darauf, dem Leser die Zusammenhänge unterschiedlicher Bereiche der Analysis zu vermitteln und so die Grundlage für ein umfassenderes Verständnis zu schaffen. Das Werk zeichnet sich durch seine wissenschaftliche Prägnanz und Genauigkeit aus und hat damit die Entwicklung der modernen Analysis in nachhaltiger Art und Weise beeinflusst. Der "Baby-Rudin" gehört weltweit zu den beliebtesten Lehrbüchern der Analysis und ist in 13 Sprachen übersetzt. 1993 wurde es mit dem renommierten Steele Prize for Mathematical Exposition der American Mathematical Society ausgezeichnet. Übersetzt von Uwe Krieg.

Lie Groups

Author: Wulf Rossmann
Publisher: Oxford University Press on Demand
ISBN: 9780199202515
Size: 24.80 MB
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Lie Groups is intended as an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analysed in detail, first with elementary matrix methods, then with the help of the structural tools typical of thetheory of semisimple groups, such as Cartan subgroups, roots, weights, and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when needed, in connection with homogeneous spaces, and the elements of differential and integral calculus on manifolds are presented, with special emphasis on integration on groups and homogeneous spaces. Representation theory starts from first principles, such as Schur's lemma and its consequences, and proceeds from there to the Peter-Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups.

Lie Gruppen Und Lie Algebren

Author: Joachim Hilgert
Publisher: Springer-Verlag
ISBN: 3322802701
Size: 55.85 MB
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Dieses Buch versteht sich als Einführung in die Theorie der Lie-Gruppen. Der Begriff der Lie-Gruppen wird ausgehend von den einfachsten Beispielen, den Matrizengruppen, entwickelt. Eine große Anzahl von Problemen für Lie-Gruppen kann man durch Übertragung auf die zugehörigen Lie-Algebren lösen. Dies ist der Leitgedanke des Buches. Vorausgesetzt werden Kenntnisse in der Linearen Algebra, der Differentialrechnung mehrerer Variablen und der elementaren Gruppentheorie.

Introduction To Lie Algebras And Representation Theory

Author: J.E. Humphreys
Publisher: Springer Science & Business Media
ISBN: 1461263980
Size: 65.32 MB
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This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.

Lie Groups Beyond An Introduction

Author: Anthony W. Knapp
Publisher: Springer Science & Business Media
ISBN: 9780817642594
Size: 57.98 MB
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This book takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. The book initially shares insights that make use of actual matrices; it later relies on such structural features as properties of root systems.