Introduction to Lie algebras
Lecturers and Teaching Assistants
Prof. Maria Gorelik
Edward Medina Guerra
Course Schedule and Location
Thursday, 13:15 - 16:15, Ziskind, Rm 1
Field of Study, Course Type and Credit Points
Mathematics and Computer Science: Lecture; Elective; Regular; 3.00 points
Chemical Sciences: Elective; 3.00 points
This course will be held by hybrid learning.
A course in Linear Algebra (including the Jordan forms).
Attendance and participation
Estimated Weekly Independent Workload (in hours)
The course will work using the following scheme:
the lecture notes and the homework assignments will be sent each week:
the homework solutions should be sent by email to Maria or left in her mailbox.
Please, send an email to Maria if you would like to receive the lecture notes and
the homework assignments.
In order to pass the course one has to submit all homework assignments with at least half of the problems solved and take a final exam. The participants will have an opportunity to discuss the homework assignment during the practical sessions which will be held at least 3 days before the deadline of the assignment.
- Definition of a Lie algebra, examples.
- Representations, representation theory of sl(2)
- Solvable and nilpotent Lie algebras, Engel's Theorem, Lie's Theorem
- Simplicity and semi-simplicity, Killing form, Cartan's criterion
- Complete reducibility of representations, Casimir element
- Root systems, Weyl group
- Cartan matrix, Dynkin diagrams
- Classification of complex semi-simple Lie algebras
- Weyl Character formula
Upon successful completion of this course students should be able to
demonstrate an understanding of the concepts of structure theory of complex semisimple Lie algebras and their representations.
Suggested reading: J. E. Humphreys "Introduction to Lie Algebras and Representation Theory"