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Hopf Algebras
(dt. Hopf-Algebren)

Level, degree of commitment Specialization module, depends on importing study program
Forms of teaching and learning,
Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements
9 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination (individual examination)
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics.
Origin M.Sc. Mathematics
One semester,
Regularly alternating with other specialization modules
Person in charge of the module's outline Prof. Dr. István Heckenberger


  • Tensors
  • Coalgebras, bialgebras, Hopf algebras
  • Sweedler notation
  • Duality of moduli and comoduli as well as of algebras and coalgebras
  • co-simple koalgebras
  • integrals
  • fundamental theorem for Hopf moduli
  • the Drinfeld dual
  • Yetter-Drinfeld moduli and braided tensor categories

Qualification Goals

The students

  • know elements of the theory of Hopf algebras,
  • view familiar abstract mathematical structures from a new perspective,
  • are able to analyze unfamiliar abstract structures using unfamiliar methods,
  • are proficient in dealing with tensors,
  • have deepened mathematical working methods (developing mathematical intuition and its formal justification, abstraction, proof),
  • have improved their oral communication skills in lecture and tutorials by practicing free speech in front of an audience and in discussion.


None. The competences taught in the following modules are recommended: either Algebra [Bachelor Module] or Algebra [Lehramt Module].


The module can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • M.Sc. Mathematics
  • LAaG Mathematics

When studying M.Sc. Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.

The module can also be used in other study programs (export module).

The module is assigned to Pure Mathematics. Further information on eligibility can be found in the description of the study area.

Recommended Reading

  • Sweedler, M.E., Hopf Algebras, Benjamin, 1969
  • Montgomery, S., Hopf Algebras and Their Actions on Rings, AMS, 1993
  • Radford, D.E., Hopf Algebras, World Scientific, 2012
  • Heckenberger, I., Schneider, H.J., Hopf Algebras and Root Systems, AMS, 2020

Please note:

This page describes a module according to the latest valid module guide in Winter semester 2023/24. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

  • Winter 2016/17 (no corresponding element)
  • Summer 2018 (no corresponding element)
  • Winter 2018/19 (no corresponding element)
  • Winter 2019/20 (no corresponding element)
  • Winter 2020/21 (no corresponding element)
  • Summer 2021 (no corresponding element)
  • Winter 2021/22 (no corresponding element)
  • Winter 2022/23 (no corresponding element)
  • Winter 2023/24

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.