University at Buffalo

Department of Mathematics






College of Arts and Sciences

Department of Physics


Yorck Sommerhäuser


Topics in Algebra: Hopf Algebras

  • Spring semester 2014
  • Course: MTH 819
  • Instructor: Y. Sommerhäuser
  • Schedule:
    • Time: Tue, Thu, 12:30 pm-1:50 pm
    • Room: Math 235
  • Office hours of Y. Sommerhäuser: Mon 12:00 pm-1:00 pm, Tue 4:00 pm-5:00 pm, 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.
  • 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:

Former courses

Last modified: September 7, 2016