Prof. Dr. Moritz Weber
Daniel Gromada
Reading seminar on quantum groups and Hopf algebras
(Winter term 2018/2019)News
Time and Place
Wednesday, 1416, SR6 (room 217, building E2 4)
Schedule:

Contents
Symmetry is a central concept in mathematics and science; many groundbreaking discoveries relied on the studyof symmetry. Mathematically, symmetries are understood in the first place as an invariance under an action of a
group. However, the developments of modern mathematics and quantum physics revealed the need to go beyond
groups in order to capture a new understanding of symmetry. This was the birth of quantum groups in the 1980's,
the pioneers being amongst others Drinfeld and Jimbo for algebraic approaches and Woronowicz for an analytic
or topological one.
In this seminar, we will address the following questions and topics:
 (Quantum) groups as (quantum) symmetries of (quantum) spaces
 Woronowicz's compact (matrix) quantum groups and their main properties
 Hopf algebras, their main properties and their links to compact quantum groups
 Examples of compact (matrix) quantum groups and of Hopf algebras
Announcement of the seminar
References
 T. Timmermann, An invitation to quantum groups and duality, EMS, 2008 (book).
 S. Neshveyev, L. Tuset, Compact quantum groups and their representation categories, SMF, 2013 (book).
 S.L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys.,1987 (article).
 S.L. Woronowicz, TannakaKrein duality for compact matrix pseudogroups. Twisted SU(N) groups
Invent. Math., 1988 (article).  M. Weber,
Introduction to compact (matrix) quantum groups and BanicaSpeicher (easy) quantum groups,
Indian Academy of Sciences. Proceedings. Mathematical Sciences, Vol. 127, Issue 5, pp 881933, Nov 2017.
(survey article)
 A. Klimyk, K. Schmüdgen, Quantum groups and their representations, Texts and Monographs in Physics,
1997 (book).  Chr. Kassel, Quantum groups, Graduate Texts in Mathematics 155, 1995 (book).
 Sh. Majid, Foundations of quantum group theory, Cambridge, 1995 (book).
 A. Maes, A. Van Daele, Notes on compact quantum groups, Nieuw Arch. Wisk. (4) 16, no.12, 1998
(survey article).  J. Kustermans, L. Tuset, A survey of C*algebraic quantum groups. I. / II., Irish Math. Soc. Bull. No. 43/44,
1999/2000 (survey article).
Last update: 14 November 2018 Moritz Weber  Impressum 