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Yorck Sommerhäuser
Courses
Topics in Algebra: Hopf Algebras
 Spring semester 2014
 Course: MTH 819
 Instructor: Y. Sommerhäuser
 Schedule:
 Time: Tue, Thu, 12:30 pm1:50 pm
 Room: Math 235
 Office hours of Y. Sommerhäuser:
Mon 12:00 pm1:00 pm, Tue 4:00 pm5:00 pm, Thu 4:00 pm5:00 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 LarsonRadford theorem on the involutivity of semisimple Hopf algebras over fields of characteristic zero, the NicholsZoeller 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: 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.
 Grading:
 A: 90 percent (or better)
 A: 88 percent (or better)
 B+: 86 percent (or better)
 B: 80 percent (or better)
 B: 78 percent (or better)
 C+: 76 percent (or better)
 C: 70 percent (or better)
 C: 68 percent (or better)
 D+: 66 percent (or better)
 D: 60 percent (or better)
 Syllabus.
 Exercise sheets:
