MATH 747
LIE ALGEBRAS
Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g. MATH 541 and 542 or MATH 741 and 742 ) are strongly recommended.
Topics
- tangent spaces
- exponentials
- Baker-Campbell-Hausdorff formula
- (nilpotent
- solvable
- semisimple) Lie algebras
- Engel's and Lie's theorems
- Levi decomposition
- Killing form
- sl(2)-representations
- root systems
- Dynkin diagrams
- Weyl groups
- Cartan and Borel subalgebras
- Serre's theorem
Topics explicitly listed in official catalogue description
Prerequisites & course information
Requisites: Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program Course Designation: Grad 50% - Counts toward 50% graduate coursework requirement Repeatable for Credit: No Last Taught: Spring 2024
Sources
- Course catalogue ↗2026-2027