Presentation: written work should be done on one side only of 8.5''x11'' paper with smooth edges. Each problem should begin a new page.
Deadlines: papers should be turned in outside of Jones 130. Extensions may be granted if requested at least forty-eight hours before the due date. Late homework will not be accepted.
| Date | Topic | |
| 1 | 1/22 | Overview of the material |
| 2 | 1/27 | Endomorphisms, polynomials and the Jordan-Chevalley decomposition |
| 1/29 | Lie algebras: definitions | |
| 3 | 2/03 | Examples, structure constants |
| 2/05 | Morphisms and quotients | |
| 4 | 2/10 | Representations, centralisers and normalisers, $\mathfrak{sl}(2)$ |
| 2/12 | The adjoint representation, the derived algebra | |
| 5 | 2/17 | Solvable Lie algebras |
| 2/19 | Solvable radicals and semisimplicity | |
| 6 | 2/26 | Lie's theorem |
| 2/28 | Nilpotent Lie algebras | |
| 7 | 3/02 | Engel's Theorem |
| 3/04 | Consequences of Engel's Theorem, duality | |
| 8 | Spring Break | |
| 9 | 3/16 | No class |
| 3/18 | Online meeting | |
| 10 | 3/23 | Cartan's criterion for solvability - online |
| 3/25 | Cartan's criterion for semi-simplicity - online | |
| 11 | 3/30 | Structure of semisimple Lie algebras - online |
| 4/01 | Basic notions of Representation Theory - online | |
| 12 | 4/06 | Complete reducibility, Schur's Lemma - online |
| 4/08 | Representations of $\mathfrak{sl}(2)$ - online | |
| 13 | 4/13 | Root space decomposition - online |
| 4/15 | Properties of roots - online | |
| 14 | 4/20 | Concrete root systems, I - online |
| 4/22 | Concrete root systems, II - online | |
| 15 | 4/27 | Concrete root systems, III - online |
| 4/29 | Root theory for $\mathfrak{sl}(3,\mathbb{C})$ - online |