6 ECTS credits
150 h study time

Offer 1 with catalog number 4013289FNR for all students in the 2nd semester at a (F) Master - specialised level.

Semester
2nd semester
Enrollment based on exam contract
Impossible
Grading method
Grading (scale from 0 to 20)
Can retake in second session
Yes
Taught in
Dutch
Faculty
Faculty of Science and Bio-engineering Sciences
Department
Mathematics
Educational team
Stefaan Caenepeel (course titular)
Joost VERCRUYSSE
Activities and contact hours

30 contact hours Lecture
30 contact hours Seminar, Exercises or Practicals
Course Content

The tensor product; algebras, coalgebras, bialgebras, Hopf algebras. The Sweedler notation. Examples of Hopf algebras. Bialgebras and Hopf algebras from the point of view of monoidal categories. Modules and comodules. Integral theory for Hopf algebras and the fundamental theorem of Hopf modules. Coideals and Hopf ideals. Construction of Hopf algebras by Ore extensions. Comodule algebras. Corings; Galois theory for corings; Hopf-Galois extensions; Morita Theory; Strongly graded rings. Examples from noncommutative geometry.

Course material
Digital course material (Required) : Hopf algebras and quantum groups, S. Caenepeel and J. Vercruysse, pointcarre en webpagina S. Caenepeel
Handbook (Recommended) : Quantumgroups, VUB bibliotheek 511.6 G KASS 95, C. Kassel, Springer-Verlag, Berlin, 9781461269007, 1995
Handbook (Recommended) : Hopf algebras, an introduction, VUB bibliotheek 511G DASC 2001, S. Dascalescu, C. Nastasescu, S. Raianu, Dekker, New York, 9780824704810, 2001
Additional info

Course notes will be available.
ADDITIONAL STUDY MATERIAL
S. Dascalescu, C. Nastasescu, S. Raianu,  Hopf algebras, an introduction, Dekker, New York, 2001, ISBN 0-8247-0481-9, VUB library 511G DASC 2001
C. Kassel,  Quantum groups, Springer-Verlag, Berlin, 1995, ISBN 0-387-94370-6, VUB library 511.6 G KASS 95

Learning Outcomes

General competencies

The main aim is to acquire a deeper understanding of the algebraic structure called Hopf algebra. Studying Hopf algebras, we face new mathematical techniques (using the tensor product, the Sweedler notation, working with monoidal categories,...). The aim is to get used to this new methods. Applications and relations to other mathematical discisplines (Galois theory, category theory, ring theory) will be discussed.

Grading

The final grade is composed based on the following categories:
Other Exam determines 100% of the final mark.

Within the Other Exam category, the following assignments need to be completed:

  • Mondeling theorie en oefeninge with a relative weight of 1 which comprises 100% of the final mark.

Additional info regarding evaluation

Oral exam about theory and exercises (100 %)

Allowed unsatisfactory mark
The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.

Academic context

This offer is part of the following study plans:
Master of Mathematics: Fundamental Mathematics (only offered in Dutch)