Hopf Algebras

Fall semester 2024
Course: MATH 6329
Course record number: 43688
Instructor: Y. Sommerhäuser
Schedule:
- Time: Tue, Thu 2:00 pm-3:15 pm
- Room: HH 3013
- Virtual room: Memorial Webex page
Office hours of Y. Sommerhäuser:
- Time: Mon 3:15 pm-5:15 pm, Thu 3:45 pm-5:45 pm and by appointment
- Room: HH 3007
Textbook: Y. Sommerhäuser: MATH 6329 Course Manual, 2nd ed., Memorial University, St. John's, 2022
Outline: We discuss Hopf algebras and Hopf modules, integrals, Frobenius algebras, Maschke's theorem for Hopf algebras, modular functions and elements, Radford's formula for the fourth power of the antipode, trace formulas for integrals, the Larson-Radford theorem on the involutivity of semisimple Hopf algebras over fields of characteristic zero, the Nichols-Zoeller freeness theorem, the class equation for Hopf algebras, the Drinfel'd double, the exponent of a Hopf algebra, and Cauchy's theorem for Hopf algebras.
Homework: Every Tuesday, a weekly exercise sheet will be handed out. This has to be submitted in class on the following Tuesday. There will be no exercise sheets during the last two weeks of the semester.
Examinations: There will be no examinations. The final mark will be based entirely on the score of the exercise sheets.
Syllabus.
Exercise sheets:
- Sheet 1
- Sheet 2
- Sheet 3
- Sheet 4
- Sheet 5
- Sheet 6
- Sheet 7
- Sheet 8
- Sheet 9
- Sheet 10

Former courses
Last modified: November 15, 2024