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Instructors: Prof. Dr. Christoph Schweigert
Event type:
Lecture
Displayed in timetable as:
M-VAlg-V
Hours per week:
4
Language of instruction:
English
Min. | Max. participants:
- | -
Comments/contents:
Content:
1) Hopf algebras and their representation categories
2) Finite-dimensional Hopf algebras
3) Quasi-triangular Hopf algebras and braided categories
4) Topological field theories and quantum codes
Updated information on the class can be found at
https://www.math.uni-hamburg.de/home/schweigert/ws22/hopf.html
Learning objectives:
We present an introduction to Hopf algebras over a field and their applications to topological field theories. The study of Hopf algebras (sometimes also known as quantum groups) is a very active field, relating algebra, representation theory and mathematical physics. Hopf algebras and topological field theories have applications in topology, string theory, quantum gravity and quantum information theory.
Special emphasis in this course will be on complex finite-dimensional Hopf algebras: their structure theory, examples and their representation categories. As an application, we present constructions of topological field theories.
Didactic concept:
This lecture aims at students in the master programs of mathematics, mathematical physics and physics. It is accessible to motivated bachelor students as well.
Prerequisites are a good knowledge of linear algebra. Some notions from algebra (in particular about groups and algebras) or the theory of Lie algebras are helpful, but not indispensable.
Per default the course will be held in English (but it can be in German if everyone is sufficiently fluent).
Literature:
Apart from lecture notes available at
http://www.math.uni-hamburg.de/home/schweigert/skripten.html
S. Dascalescu, C. Nastasescu, S. Raianu, Hopf Algebras. An Introduction. Monographs
and Textbooks in Pure and Applied Mathematics 235, Marcel-Dekker, New-York, 2001.
C. Kassel, Quantum Groups, Graduate Texts in Mathematics 155, Springer, Berlin, 1995.
C. Kassel, M. Rosso, Vl. Turaev: Quantum groups and knot invariants.
Panoramas et Synthèses, Soc. Math. de France, Paris, 1993
S. Montgomery, Hopf algebras and their actions on rings, CMBS Reg. Conf. Ser. In Math.
82, Am. Math. Soc., Providence, 1993.
Hans-Jürgen Schneider, Lectures on Hopf algebras, Trabajos de Matemática 31/95,
FaMAF, 1995. http://www.famaf.unc.edu.ar/series/pdf/pdfBMat/BMat31.pdf
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