The aim of the course is to give the students an elementary introduction to the Theory of Lie Algebras, and the ability to solve some simple problems regarding Lie Algebras. The ultimate goal of the course is the classification of complex semisimple Lie algebras, a beautiful example of classification of a family of algebraic structures, which is important also for other branches of algebra. The student is expected to understand the results and the proofs presented throughout the course, within the frame of the whole theory, and to be able to solve some problems concerning the algebraic structure of Lie algebras.
Course Prerequisites
Linear Algebra, Algebra 1 (basics of group theory)
Teaching Methods
Lectures and exercises
Assessment Methods
The final exam consist of a first written part, and an oral examination: the written part is a short exercise (the student is expected to solve it in about 20') aimed at verifying the ability of the student to apply the notions and the techniques learned throughout the course to "concrete" problems concerning small Lie algebras; the oral examination is right after the written part.
Contents
The aim of the course is to give an elementary introduction to the theory of Lie Algebras. Starting from the definition of a Lie Algebra, we will study Lie algebras of low dimension, and solvable Lie algebras. The ultimate goal (depending on the time available for the course) of the course is to prove the classification of complex simple Lie algebras via root systems. Detailed program: - Lie algebras: definition and examples - Lie algebras of low dimension (?) - Solvable and nilpotent Lie algebras - Engel's and Lie's Theorem - Representations of sl_2(C) - Cartan's criteria - Roots systems (?) - Classification of simple algebras
Course Language
English
More information
The reception with the teacher is by appointment: contact at claudio.quadrellił@uninsubria.it
