Quantum Groups

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Department of Mathematics

Synopsis:

The subject deals with mathematical analysis of integrable model solutions. It introduces students to basic concepts and constructions in quantum groups.

Requirements:

Syllabus of lectures:

1. Rehearsal of Lie algsebra and Lie groups.2. Hopf algebras.3. Classical and quantum Yang-Baxter equation.4. Poisson algebras.5. Drinfeld-Jimbe's formulation of quantum groups.6. Woronowicz formulation of quantum groups.7. Basics of non-commutative geometry.8. Applications in mathematics and mathematical physics.9. Integrative models.

Syllabus of tutorials:

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Study materials:

Key references: [1] A. Klimyk, K. Schmudgen: Quantum Groups and Their Representation, Springer, Berlin, 1997.[2] P. Woit,Quantum Theory, Groups and Representations: An Introduction, Springer, 2017.Recommendedreferences:[3] G. Lustig: Introduction to Quantum Groups, Birkhauser, Boston, 1993.[4] Ch. Kassell: Quantum Groups, Graduate Texts in Mathematics, Springer, New York, 2012.[5] E. Abe: Hopf algebras, Cambridge Tracts in Mathematics, Univ. Press. Cambridge, 2008.[6] J. Dixmier: Enveloping Algebra, North-Holland, Amsterdam, 1997.[7] A. Connes: Non-Commutative Geometry, Academic Press, New York 1994.

Note:

Time-table for winter semester 2023/2024:

Time-table is not available yet

Time-table for summer semester 2023/2024:

Time-table is not available yet

The course is a part of the following study plans: