9780387900520-0387900527-Introduction to Lie Algebras and Representation Theory (Graduate Texts in Mathematics (9))

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

ISBN-13: 9780387900520
ISBN-10: 0387900527
Edition: Softcover reprint of the original 1st ed. 1972
Author: Humphreys, J.E.
Publication date: 1973
Publisher: Springer
Format: Paperback 186 pages
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Book details

ISBN-13: 9780387900520
ISBN-10: 0387900527
Edition: Softcover reprint of the original 1st ed. 1972
Author: Humphreys, J.E.
Publication date: 1973
Publisher: Springer
Format: Paperback 186 pages

Summary

Acknowledged authors Humphreys, J.E. wrote Introduction to Lie Algebras and Representation Theory (Graduate Texts in Mathematics (9)) comprising 186 pages back in 1973. Textbook and eTextbook are published under ISBN 0387900527 and 9780387900520. Since then Introduction to Lie Algebras and Representation Theory (Graduate Texts in Mathematics (9)) textbook was available to sell back to BooksRun online for the top buyback price or rent at the marketplace.

Description

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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