AIS on Lie Algebras (4-23 July 2011) CMI-IMSc, Chennai
Videos of all lectures on YouTube
Raghavan's Page Viswanath's Page
This page is for the participants in the above mentioned school. In some of the exercise sets we will directly write down the exercise number from Humphrey's book, which is the text-book we are following here.
Exercise Set 1(Automorphisms and Derivations)
Exercise set 2 (Tensor Products)
a paper on Jordan-Chevalley decomposition in finite dimensional Lie algebras
Exercise set 3 (PBW Theorem)
Exercise set 4 (Root Systems)
Cartan Decomposition of Classical Lie Algebras (taken from the book "Introduction to Lie Algebras" by Erdmann & Wildon)
Exercise set 5 (Representations of sl(2))
Exercise set 6 (nilpotent & solvable Lie Algebra)
Roots Systems (Lectures by Viswanath and notes taken by Shripad Garge)
Exercise set 7 (Complete Reducibility)
Exercise set 8 (The Weyl Group)
Exercise set 9 (Representations of Lie Algebras)
Notes for Lectures by Anupam Singh
Exercise set 10 (Classification of Root Systems)
Exercise set 11 (Affine Lie Algebras)
Exercise set 12 (Affine Lie Algebras - 2)
Exercise set 13 (Serre's Theorem and Automorphisms of Lie Algebra)
Exercise set 14 (Affine Lie Algebras - 3)
Photographs from a day trip to Kanchipuram
Lie Algebra review (by Raghavan, notes taken by Anupam)
Exercise set 15 (Solvable groups and Cartan decomposition)
Exercise set 16 (Chevalley Groups)
Exercise set 17 (Chevalley Groups - II)
References :
1. Introduction to Lie Algebras and Representation Theory : Humphreys
2. Lie Algebras of Finite and Affine Type : Carter
3. Lie Groups beyond an Introduction : Knapp
4. Introduction to Lie Algebras : Erdmann and Wildon
5. Infinite Dimensional Lie Algebras : Kac
6. Lie Groups and Lie Algebras : Bourbaki
7. Representation of Semisimple Lie algebras in the BGG category O : Humphreys
Some interesting papers :