Introduction to Lie Algebras and Representation Theory by J.E. 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...

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Bibliographic Details
Main Author:	Humphreys, J.E (Author)
Corporate Author:	SpringerLink (Online service)
Format:	eBook
Language:	English
Published:	New York, NY : Springer New York : Imprint: Springer, 1972.
Edition:	1st ed. 1972.
Series:	Graduate Texts in Mathematics, 9 Springer eBook Collection.
Subjects:	Algebra. Electronic resources (E-books)
Online Access:	Click to view e-book
Holy Cross Note:	Loaded electronically. Electronic access restricted to members of the Holy Cross Community.

Table of Contents:

I. Basic Concepts
1. Definitions and first examples
2. Ideals and homomorphisms
3. Solvable and nilpotent Lie algebras
II. Semisimple Lie Algebras
4. Theorems of Lie and Cartan
5. Killing form
6. Complete reducibility of representations
7. Representations of sl (2, F)
8. Root space decomposition
III. Root Systems
9. Axiomatics
10. Simple roots and Weyl group
11. Classification
12. Construction of root systems and automorphisms
13. Abstract theory of weights
IV. Isomorphism and Conjugacy Theorems
14. Isomorphism theorem
15. Cartan subalgebras
16. Conjugacy theorems
V. Existence Theorem
17. Universal enveloping algebras
18. The simple algebras
VI. Representation Theory
20. Weights and maximal vectors
21. Finite dimensional modules
22. Multiplicity formula
23. Characters
24. Formulas of Weyl, Kostant, and Steinberg
VII. Chevalley Algebras and Groups
25. Chevalley basis of L
26. Kostant’s Theorem
27. Admissible lattices
References
Afterword (1994)
Index of Terminology
Index of Symbols.

Introduction to Lie Algebras and Representation Theory by J.E. Humphreys.

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