Representation theory III - Quantum groups

MATH-534 / 5 credits

Teacher: Negut Andrei

Language: English

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

One written homework (15% of the grade) and a written exam (85% of the grade).

Supervision

Assistants Yes
Forum Yes

Resources

Bibliography

C. Kassel, "Quantum groups"

Ressources en bibliothèque

Moodle Link

In the programs

  • Semester: Spring
  • Exam form: Written (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: Written (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: Written (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

Reference week

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