Introduction to Lie Algebras

Prerequisites: Basic Linear Algebra and the basic concepts of ring and body theory.

We will study the basic concepts of structure theory and representations of finite dimension Lie algebras on complex numbers.
We will define ideals, homomorphisms, representations, etc. Then we will study the basic structure theorems: Killing form, Casimir elements, root systems, classification of simple algebras. Finally we will study the theory of finite dimension representations: characters, Weyl formula, etc. The course is exclusively algebraic but connections with Lie group theory and geometry will be mentioned.

References:
HUMPHREYS, J.E. – Introduction to Lie algebras and representation theory (Springer).
KNAPP’S, A. W. – Lie groups beyond an introduction (Birkhäuser).
KAC, V. G. MIT class notes http://math.mit.edu/classes/18.745/classnotes.html

Note: This course is offered as a master’s degree. At the PhD, she has additional requirements.

* Standard program. The teacher has the autonomy to make any changes