Representation theory III - Quantum groups
Summary
This course serves as an introduction to the theory of quantum groups, with particular emphasis on using their R-matrices to obtain link invariants.
Content
This is a third semester course in representation theory, which succeeds the theory of semisimple Lie algebras. We will define quantum groups as deformations of Lie algebras, and construct R-matrices for quantum groups using the formalism of Hopf algebras. Using these R-matrices, we will obtain invariants of links, such as the celebrated Jones polynomial that arises from the case of sl_2.
Keywords
Quantum groups, Hopf algebras, R-matrices, Yang-Baxter equation, link invariants
Learning Prerequisites
Required courses
MATH-429 Representation theory II - Lie algebras, or equivalent
Learning Outcomes
By the end of the course, the student must be able to:
- Formulate the main concepts and theorems defined in the course
- Theorize the role of quantum groups in the theory
- Compute R-matrices for simple quantum groups
Expected student activities
Students are expected to attend all lectures, read all lecture notes and participate in all problem sessions
Assessment methods
Weekly homework (100%)
Supervision
| Assistants | Yes |
| Forum | Yes |
Resources
Bibliography
C. Kassel, "Quantum groups"
Ressources en bibliothèque
Moodle Link
In the programs
- Semester: Spring
- Exam form: During the semester (summer session)
- Subject examined: Representation theory III - Quantum groups
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: During the semester (summer session)
- Subject examined: Representation theory III - Quantum groups
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: During the semester (summer session)
- Subject examined: Representation theory III - Quantum groups
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional