Introduction to Lie Algebras and Representation Theory: 9 (Graduate Texts in Mathematics, 9) - Softcover

Humphreys, J.E.

 
9780387900520: Introduction to Lie Algebras and Representation Theory: 9 (Graduate Texts in Mathematics, 9)
Softcover
ISBN 10: 0387900527 ISBN 13: 9780387900520
Verlag: Springer, 2013

Inhaltsangabe

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.

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Reseña del editor

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.

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Verlag
Springer
Erscheinungsdatum
2013
Sprache
Englisch
ISBN 10 
0387900527
ISBN 13 
9780387900520
Einband
Tapa blanda
Anzahl der Seiten
196
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
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Weitere beliebte Ausgaben desselben Titels

9780387900537: Introduction to Lie Algebras and Representation Theory: 9 (Graduate Texts in Mathematics, 9)

Vorgestellte Ausgabe

ISBN 10:  0387900535 ISBN 13:  9780387900537
Verlag: Springer, 1997
Hardcover