Seminar Series-CSUF May 22-26  INTRODUCTION TO LIE ALGEBRAS  

May 22-26 2:00-4:00 PM LH-322 (syllabus)

Books and Notes on Lie algebras (here)

Introduction to Lie Algebras and representation theory-James E. Humphreys (186pp) (click here)

Introduction to Lie Algebras and representation theory-James E. Humphreys-Chapter 1 (14pp) (click here)

Introduction to Lie Algebras and representation theory-James E. Humphreys-Chapter 2 (27pp) (click here)

First meeting Part 1, Monday May 22. Definitions and first concepts (informal notes: Humphreys pages 1-5)(click here)

definition, Jacobi identity, isomorphism, subalgebra

End(V), gl(V)=End(V)^-, linear Lie algebra

Classical Lie algebras

derivation, inner derivation, adjoint representation

abelian Lie algebras, structure constants

Lie algebras of dimensions 1 and 2

First meeting, Part 2 Monday May 22. Ideals and Homomorphisms (informal notes: Humphreys pages 6-9)(click here)

ideal, center, derived algegra

simple Lie algebra, sl(2,F) is simple

quotient Lie algebra

normalizer and centralizer of a subset

homomorphism, homomorphism theorems

representation, automorphism group

exponential of a nilpotent derivation, inner automorphism

First meeting Part 2 REVISITED Ideals and Homomorphisms (more informal notes: Humphreys pages 6-9) (Correction: ON PAGE 8 THE LAST LINE SHOULD BE lambda_(exp x) NOT exp lambda_x)(click here)

Discussion of Assignment 1-Part 1 #1-5(click here)

Discussion of Assignment 1-Part 2 #6-9(click here)

Discussion of Assignment 1-Part 3 #10-12 (forthcoming) (click here)

Discussion of Assignment 2-Part 1 #1-9 (except #4,6) (click here)

First meeting Part 3, Monday May 22. Solvable and Nilpotent Lie Algebras (informal notes: Humphreys pages 10-14)(click here)

First meeting Part 3 REVISITED Solvable and Nilpotent Lie Algebras (more informal notes: Humphreys pages 10-14)(click here)

Discussion of Assignment 3 #1-10 (click here)

Further Discussion of Assignment 3 #7-10 (Correction: ON PAGE 2 IN THE FOURTH LINE FROM THE BOTTOM, IT SHOULD BE N_L(K) IS NOT EQUAL TO L)(click here)

Second meeting Tuesday May 23. Theorems of Lie and Cartan (informal notes: Humphreys pages 15-20)(click here)

Second meeting REVISITED Theorems of Lie and Cartan (informal notes-part 1 Humphreys pages 15-18)(click here)

Second meeting REVISITED Theorems of Lie and Cartan (informal notes-part 2 Humphreys pages 19-20)(click here)

Third meeting Part 1, Wednesday May 24. Killing Form (informal notes: Humphreys pages 21-25)(click here)

Third meeting Part 2, Wednesday May 24. Complete reducibility of representations (informal notes: Humphreys pages 25-31)(click here)

Fourth meeting Part 1, Thursday May 25. Representations of sl(2,F) (informal notes: Humphreys pages 31-35)(click here)

Fourth meeting Part 2, Thursday May 25. Root space decomposition (informal notes: Humphreys pages 35-42)(click here)

Fifth meeting Part 1, Friday May 26. TBA(click here)

Fifth meeting Part 2, Friday May 26. TBA(click here)