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.
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 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
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.
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:
Oral exam about theory and exercises (100 %)
This offer is part of the following study plans:
Master of Mathematics: Fundamental Mathematics (only offered in Dutch)