Introduction to Lie algebras and representation theory.

By:

Humphreys, James E

Material type: Text

TextSeries: Graduate texts in mathematics ; v. 9.Publication details: New York : Springer-Verlag, c1972.Description: xii, 171 pISBN:

9780387900537

Subject(s):

Lie algebras

DDC classification:

510 HUM

Contents:

Basic Concepts James E. Humphreys Pages 1-14 Semisimple Lie Algebras James E. Humphreys Pages 15-41 Root Systems James E. Humphreys Pages 42-72 Isomorphism and Conjugacy Theorems James E. Humphreys Pages 73-88 Existence Theorem James E. Humphreys Pages 89-106 Representation Theory James E. Humphreys Pages 107-144 Chevalley Algebras and Groups James E. Humphreys Pages 145-164 Back Matter Pages 165-177

Summary: 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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Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode
Project book	CUTN Central Library Sciences	Non-fiction	510 HUM (Browse shelf(Opens below))	Checked out to Renuka Devi V (20019T)	31/01/2024	48840

Basic Concepts
James E. Humphreys
Pages 1-14
Semisimple Lie Algebras
James E. Humphreys
Pages 15-41
Root Systems
James E. Humphreys
Pages 42-72
Isomorphism and Conjugacy Theorems
James E. Humphreys
Pages 73-88
Existence Theorem
James E. Humphreys
Pages 89-106
Representation Theory
James E. Humphreys
Pages 107-144
Chevalley Algebras and Groups
James E. Humphreys
Pages 145-164
Back Matter
Pages 165-177

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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