UPDATED JUNE 17, 2017
Independent Studies-Mathematics 199C-SPRING 2017
NONASSOCIATIVE ALGEBRA
Wednesdays 4-4:50 RH 340N
(syllabus-updated April 18, 2017)
Books and Notes on Lie algebras (updated April 26, 2017)
(here)
FORUM---Email questions from students and answers (forthcoming)
(click 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)
"FINAL EXAM" PROBLEMS (From 199A, corrected March 16, 2017)-Part 1 #1-10, Part 2 #11-20, Part 3 #21-23.
(click here)
"FINAL EXAM" PROBLEMS (From 199B-posted March 18, 2017)
This is a list of the statements of the problems assigned from chapters 5,6,7, and 8 (I have not included a "discussion" on any of the problems at this time)
(click here)
First meeting (Week 2), Monday April 10, 2017.
Definitions and first concepts (informal notes: Humphreys pages 1-5)(click here)
Second meeting (Week 3), Wednesday April 19, 2017.
Ideals and Homomorphisms (informal notes: Humphreys pages 6-9)(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)
Third meeting (Week 4), Wednesday April 26, 2017.
Solvable and Nilpotent Lie Algebras (informal notes: Humphreys pages 10-14)(click here)
Discussion of Assignment 3 #1-10 (click here)
Fourth meeting CANCELLED (Week 5), Wednesday May 3, 2017.
Theorems of Lie and Cartan (informal notes: Humphreys pages 15-20)(click here)
NO MEETING IN WEEK 5. HOWEVER, NOTE THE FOLLOWING THREE ITEMS
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 REVISITED (Week 3), April 19, 2017.
Ideals and Homomorphisms (more informal notes: Humphreys pages 6-9)
(click here)
Third meeting REVISITED (Week 4), Wednesday April 26, 2017.
Solvable and Nilpotent Lie Algebras (more informal notes: Humphreys pages 10-14)(click here)
Fourth meeting REVISITED (Week 6), Wednesday May 10, 2017.
Theorems of Lie and Cartan (informal notes-part 1 Humphreys pages 15-18)(click here)
Fourth meeting REVISITED (Week 6), Wednesday May 10, 2017.
Theorems of Lie and Cartan (informal notes-part 2 Humphreys pages 19-20)(click here)
Fifth meeting (Week 7), Wednesday May 17, 2017.
Representations of sl(2,F) (informal notes: Humphreys pages 31-35)(click here)
Sixth meeting (Week 9), Wednesday May 31, 2017.
Killing Form (informal notes: Humphreys pages 21-25)(click here)
Sixth meeting (Week 9), Wednesday May 31, 2017.
Complete reducibility of representations (informal notes: Humphreys pages 25-31)(click here)
Seventh meeting (Week 10) Wednesday June 7, 2017
Chinese Remainder Theorem (informal notes: S. Lang, Algebra 1965) pp. 63-64)(click here)
Seventh meeting (Week 10) Wednesday June 7, 2017
Jordan decomposition-continued (informal notes,revised: Erdmann-Wildon pages 192-201)(click here)
Seventh meeting (Week 10) Wednesday June 7, 2017
Abstract Jordan decomposition (informal notes: Erdmann-Wildon pages 85-88)(click here)
Seventh meeting (Week 10), Monday June 7, 2017.
Root space decomposition (informal notes: Humphreys pages 35-42)(click here)
(posted June 17) Fifth meeting REVISITED (Week 7), Wednesday May 17, 2017.
Representations of sl(2,F) (informal notes: Humphreys pages 31-35)(click here)