Hopf Algebras

Winter semester 2016
Course: MATH 6329
Instructor: Y. Sommerhäuser
Schedule:
- Time: Tue 12:00 m-12:50 pm, Thu 12:00 m-12:50 pm, Fri 1:00 pm-1:50 pm
- Room: SN 2041
Office hours of Y. Sommerhäuser: Tue, Thu 4:00 pm-5:00 pm and by appointment
Textbook: S. Montgomery: Hopf algebras and their actions on rings, 2nd revised printing, Reg. Conf. Ser. Math., Vol. 82, Am. Math. Soc., Providence, 1997
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.
Exams: There will be a midterm exam and a comprehensive final exam. The midterm exam takes place on Tuesday, February 16. The final exam takes place on Monday, April 18, at 1:00 pm at the AAC.
Homework: On Tuesday, a weekly exercise sheet will be handed out, containing three or four problems. This has to be completed until the next Tuesday. While it is allowed to collaborate on the problems, every student is required to write up his solution in his own words.
Examination criteria: The final mark will be computed using the following weights.
- Homework: 25 percent
- Midterm exam: 25 percent
- Final exam: 50 percent
Syllabus.
Exercise sheets:

Former courses
Last modified: April 19, 2020