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

Humphreys, J.E.

Hardcover

ISBN 10: 0387900535 ISBN 13: 9780387900537

Publisher: Springer, 1972

Synopsis

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.

About this title

Review

J.E. Humphreys

Introduction to Lie Algebras and Representation Theory

"An excellent introduction to the subject, ideal for a one semester graduate course."THE AMERICAN MATHEMATICAL MONTHLY

"Exceptionally well written and ideally suited either for independent reading or as a text for an introduction to Lie algebras and their representations."MATHEMATICAL REVIEWS

J.E. Humphreys

Introduction to Lie Algebras and Representation Theory

"An excellent introduction to the subject, ideal for a one semester graduate course."???THE AMERICAN MATHEMATICAL MONTHLY

"Exceptionally well written and ideally suited either for independent reading or as a text for an introduction to Lie algebras and their representations."???MATHEMATICAL REVIEWS

J.E. Humphreys

Introduction to Lie Algebras and Representation Theory

"An excellent introduction to the subject, ideal for a one semester graduate course."a "THE AMERICAN MATHEMATICAL MONTHLY

"Exceptionally well written and ideally suited either for independent reading or as a text for an introduction to Lie algebras and their representations."a "MATHEMATICAL REVIEWS

Synopsis

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 more demanding.This text grew out of lectures which the author gave at the N.S.F. Advanced Science Seminar on Algebraic Groups at Bowdoin College in 1968.

Edition details

• Publisher: Springer
• Publication date: 1972
• Language: English
• ISBN 10: 0387900535
• ISBN 13: 9780387900537
• Binding: Hardcover
• Number of pages: 186