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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Quantum Groups 1

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Code Completion Credits Range Language
01KVGR1 Z 2 2+0 Czech
Lecturer:
Tutor:
Čestmír Burdík (guarantor)
Supervisor:
Department of Mathematics
Synopsis:

Quantum Algebra was originated in the 80s in the works of professor L. D. Faddeev and the Leningrad school on the inverse scattering method in order to solve integrable models. They have many applications in mathematics and mathematical physics such as the classification of nodes, in the theory of integrable systems and the string theory.

Requirements:

Basic course of Calculus and Linear Algebra (in particular, the courses 01MA1, 01MAA2-4, 01LAP, 01LAA2, TRLA held at the FNSPE CTU in Prague).

Syllabus of lectures:

1. Motivation, coalgebras, bialgebras and Hopf algebras. 2. Q-calculus. 3 The quantum algebra U_q(sl(2) and its representations. 4. The quantum group SL_q(2) and its representations. 5. The q-Oscillator algebras and their representations. 6. Drinfeld-Jimbo algebras, 7. Finite-Dimensional representations of Drinfeld-Jimbo Algebras. 8. Quasitriangularity and universal R- matrix.

Syllabus of tutorials:
Study Objective:

Knowledge: to acquire the mathematical basis of the quantum group theory. Abilities: able to use the quantum group theory in studying integrable systems.

Study materials:

Key references: [1] Anatoli Klimyk, Konrad Schmudgen , Quantum groups and their representations.Springer-Verlag-Berlin 1997

Recommended references: [2] Podles, P.; Muller,E., Introduction to quantum groups, arXiv:q-alg/9704002. [3] Kassel, Christian (1995), Quantum groups, Graduate Texts in Mathematics,155, Berlin, New York: Springer-Verlag, MR1321145, ISBN 978-0-387-94370-1 [3] Majid, Shahn (2002), A quantum groups primer,London Mathematical Society Lecture Note Series, 292, Cambridge University Press, MR1904789, ISBN 978-0-521-01041-2, [4] Street, Ross (2007), Quantum groups, Australian Mathematical Society Lecture, Series, 19, Cambridge University Press, MR2294803, ISBN978-0-521-69524-4; 978-0-521-69524-4.

Note:
Time-table for winter semester 2019/2020:
Time-table is not available yet
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-02-16
For updated information see http://bilakniha.cvut.cz/en/predmet11370905.html