Introduction to Lie Algebras and Representation Theory by Je Humphreys

Introduction to Lie Algebras and Representation Theory by Je Humphreys

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.

SKU	Unavailable
ISBN 13	9780387900537
ISBN 10	0387900535
Title	Introduction to Lie Algebras and Representation Theory
Author	Je Humphreys
Series	Graduate Texts In Mathematics
Condition	Unavailable
Binding Type	Hardback
Publisher	Springer-Verlag New York Inc.
Year published	1973-01-23
Number of pages	173
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
Note	Unavailable