Algebra 4 Lie Algebras, Chevalley Groups, and Their Representations

✍ Scribed by Ramji Lal; Ramji Lal

• Year: 2021
• Tongue: English
• Leaves: 332
• Series: Infosys Science Foundation Series in Mathematical Sciences,
• Edition: 1st ed. 2021.
• Category: Library

✦ Table of Contents

Preface
Contents
About the Author
Notations
1 Lie Algebras
1.1 Definitions and Examples
1.2 Universal Enveloping Algebras: PBW Theorem
1.3 Solvable and Nilpotent Lie Algebras
1.4 Semi-Simple Lie Algebras
1.5 Extensions of Lie Algebras and Co-homology
2 Semi-Simple Lie Algebras and Root Systems
2.1 Root Space Decomposition
2.2 Root Systems
2.3 Dynkin Diagram and the Classification of Root Systems
2.4 Conjugacy Theorem, Existence and Uniqueness Theorems
3 Representation Theory of Lie Algebras
3.1 Theorems of Ado and Iwasawa
3.2 Cyclic Modules and Weights
3.3 Characters and Harish-Chandra's Theorem
3.4 Multiplicity Formulas of Weyl, Kostant, and Steinberg
4 Chevalley Groups
4.1 Classical Linear Groups
4.2 Chevalley Basis
4.3 Chevalley Groups
4.4 Twisted Groups
5 Representation Theory of Chevalley Groups
5.1 Language of Representation Theory
5.2 Representations of Sn, and of GL(2.q)
5.3 Steinberg Characters
5.4 Principal and Discrete Series Representations
5.5 Deligne–Lusztig Generalized Characters
Appendix Bibliography
Index