Quantum Groups 2
Code  Completion  Credits  Range  Language 

01KVGR2  Z  2  2+0  Czech 
 Garant předmětu:
 Lecturer:
 Tutor:
 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, 01MAA24, 01LAP, 01LAA2, TRLA held at the FNSPE CTU in Prague).
 Syllabus of lectures:

1. Motivation, coalgebras, bialgebras and Hopf algebras. 2. Qcalculus. 3 The quantum algebra U_q(sl(2) and its representations. 4. The quantum group SL_q(2) and its representations. 5. The qOscillator algebras and their representations. 6. DrinfeldJimbo algebras, 7. FiniteDimensional representations of DrinfeldJimbo 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.SpringerVerlagBerlin 1997
Recommended references: [2] Podles, P.; Muller,E., Introduction to quantum groups, arXiv:qalg/9704002. [3] Kassel, Christian (1995), Quantum groups, Graduate Texts in Mathematics,155, Berlin, New York: SpringerVerlag, MR1321145, ISBN 9780387943701 [3] Majid, Shahn (2002), A quantum groups primer,London Mathematical Society Lecture Note Series, 292, Cambridge University Press, MR1904789, ISBN 9780521010412, [4] Street, Ross (2007), Quantum groups, Australian Mathematical Society Lecture, Series, 19, Cambridge University Press, MR2294803, ISBN9780521695244; 9780521695244.
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: