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

Weekly homework (100%)

Supervision

Assistant.e.s 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

Reference week

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