Second meeting Tuesday May 23. Theorems of Lie and Cartan; Killing form

solvable implies common eigenvector

Lie: solvable implies upper triangular

semisimple endomorphism

Jordan-Chevalley decomposition

Cartan's criterion

Cartan: trace condition implies solvable

Second meeting Tuesday May 23-part 1 Theorem of Lie (informal notes-part 1 Humphreys pages 15-18)(click here)

Second meeting Tuesday May 23-part 2 Theorem of Cartan (informal notes-part 2 Humphreys pages 19-20)(click here)

Killing form, radical, nondegenerate

Killing form of sl(2,F)

semisimple if and only if nondegenerate

semisimple is direct sum of simple

semisimple implies every derivation is inner

abstract Jordan decomposition

Second meeting Tuesday May 23-Part 3 Killing Form (informal notes: Humphreys pages 21-25)(click here)