
Complex Geometry
65417 Lie algebras
Lecturer: 
Pawel Sosna

Time and place: 
Lecture: Tuesdays 12:1513:45 in room 1240 and Fridays 10:1511:45 in room 432
Recitations: every other Friday 10:1511:45 in room 432

Content: 
A Lie algebra is a vector space endowed with a nonassociative multiplication called Lie bracket. These objects are closely related to certain manifolds and are relevant in several areas of mathematics and mathematical physics.
The purpose of the lecture is to give an introduction to Lie algebras and their representation theory. In particular, we will study ideals, homomorphisms, solvable, simple and nilpotent Lie algebras and, if time permits, try to understand the classification of simple complex Lie algebras via their root systems.

Prerequisites: 
The main prerequisite for the course is a good understanding of linear algebra (that is, Lineare Algebra I and II). Some familiarity with basic concepts from algebra (rings, ideals,...) might be useful.
The lecture is suitable for students from the 4th semester on.

Literature: 

William Fulton and Joe Harris: "Representation theory. A first course", SpringerVerlag, New York, 1991.

James Humphreys: "Introduction to Lie algebras and representation theory", SpringerVerlag, New YorkBerlin, 1978.

Hans Samelson: "Notes on Lie algebras", SpringerVerlag, New York, 1990.

Christoph Schweigert: "Lie algebras" lecture notes (in German), available at his homepage.

Wolfgang Soergel: "Lie algebras" lecture notes (in German), available at his homepage.

Lecture notes: 
The preliminary lecture notes are here. Comments are welcome at all times.

Homework: 
Sheet 1
Sheet 2
Sheet 3
Sheet 4
Sheet 5
Sheet 6
Sheet 7
Sheet 8
Sheet 9
Sheet 10
Sheet 11
Sheet 12
Bonus Sheet

Exam: 
Oral exam. In order to qualify for the exam, you have to at least twice present solutions to the weekly exercises in the exercise classes.


