MATH 534 Lie Theory I (Lie Algebras and their representations)
The course will be mostly based on
J. Humphreys "Lie algebras and representation theory".
However, we will occasionally refer to several other sources, including:
Classes: Tue, Th 11am-12:30pm in MATX1102.
My office: Math 217.
e-mail: gor at math dot ubc dot ca
Office Hours: By
Syllabus and course outline
(This document is consistent with the university policies and contains all
the course information regarding marking, etc.)
There will be approximately bi-weekly written homework assignments in
list of problems for in-class discussion.
The last two weeks of class will be your
Possible topics and resources will soon be posted here.
Detailed Course outline
Short descriptions of each lecture and relevant additional references will be posted here as we progress.
- Tuesday September 3 :
NO CLASS -- Imagine day and qualifying exams.
Graduate Orientation at 4:30pm.
- Thursday September 5 and Tuesday
Lie algebras: motivation; overview; the basic definitions (including
homomorphisms, centre, radical, ...) The notions of nilpotent, solvable,
simple and semisimple; examples (the classical Lie algebras); the
2-dimensional Lie algebras; adjoint representation; proof that sl(2) is
simple. References: H: 1.1, 1.2, 2.1, 3.1, 3.2; 1.4, 2.2. FH: 9.1, some of
- Thursday Sep. 12 :
Lecture 3: The radical. Nilpotent and solvable Lie algebras. Engel's