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) (click here)

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

derived series, solvable Lie algebra

Example: upper triangular matrices

radical, semisimple Lie algebra

decending central series, nilpotent Lie algebra

Example: strictly upper triangular matrices

ad-nilpotent element, Engel's theorem, flag

If all elements of a Lie algebra are ad-nilpotent, then the algebra is nilpotent

A nilpotent Lie algebra can be represented by strictly upper triangular matrices

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

Discussion of Assignments 1,2,3 (click here)