Welcome to our Reading Group

We are planning to read the textbook Introduction to Finite and Infinite Dimensional Lie (Super)algebras throughout this semester. Our ambitious plan is to finish chapter 1 on finite dimensional Lie Algebra and reaching the basic of Kac-Moody algebra. The reading group will be held weekly and we will take turn present what we learned from the textbook. We will also try to do some exercises from this old class at MIT instructed by Victor Kac

Day 1: Saturday September 4th

Announcements and Agendas:

• Organizational Meeting

Day 2: Saturday September 11th

Announcements and Agendas:

• Subalgebras of Lie algebras.
• 4 families of classical Lie algebras: \(A_n, B_n, C_n, D_n\) and their bases
• Lie algebra representation definition, adjoint representation
• Engel's theorem

Day 3: Saturday September 25th

Announcements and Agendas:

• Lie's Theorem
• Lie's Lemma

Day 4: Saturday October 2nd

Announcements and Agendas:

• Generalized weighted space and eigenspace
• Zariski topology and regular element

Day 5: Saturday October 9th

Announcements and Agendas:

• Cartan subalgebra

Day 6: Saturday October 16th

Announcements and Agendas:

• Killing form