Quantum Groups

1. Front Matter

   Pages I-XII

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2. On some unsolved problems in quantum group theory

   • V. G. Drinfeld

   Pages 1-8

3. Quantum symmetry

   • Murray Gerstenhaber, Anthony Giaquinto, Samuel D. Schack

   Pages 9-46

4. Yang-Baxter equation and deformation of associative and Lie algebras

   • D. Gurevich, V. Rubtsov

   Pages 47-55

5. Quantum G-spaces and Heisenberg algebra

   • L. I. Korogodsky, L. L. Vaksman

   Pages 56-66

6. Real and imaginary forms of quantum groups

   • Vladimir Lyubashenko

   Pages 67-78

7. Rank of quantum groups and braided groups in dual form

   • Shahn Majid

   Pages 79-89

8. Yangians of the “strange” lie superalgebras

   • M. L. Nazarov

   Pages 90-97

9. Askey-wilson polynomials as spherical functions on SU _q(2)

   • Masatoshi Noumi, Katsuhisa Mimachi

   Pages 98-103

10. Twisted yangians and infinite-dimensional classical Lie algebras

    • G. I. Olshanskii

    Pages 104-119

11. Differential graded Lie algebras, quasi-hopf algebras and higher homotopy algebras

    • Jim Stasheff

    Pages 120-137

12. Quantum deformation of the flag variety

    • Earl J. Taft

    Pages 138-141

13. Zonal spherical functions on quantum symmetric spaces and MacDonald's symmetric polynomials

    • Kimio Ueno, Tadayoshi Takebayashi

    Pages 142-147

14. Hidden quantum groups inside Kac-Moody algebras

    • A. Alekseev, L. Faddeev, M. Semenov-Tian-Shansky

    Pages 148-158

15. Liouville theory on the lattice and universal exchange algebra for bloch waves

    • O. Babelon

    Pages 159-175

16. Non-local currents in 2D QFT: An alternative to the quantum inverse scattering method

    • Denis Bernard, André Leclair

    Pages 176-196

17. Induced representations and tensor operators for quantum groups

    • L. C. Biedenharn, M. A. Lohe

    Pages 197-209

18. Affine toda field theory: S-matrix vs perturbation

    • H. W. Braden, E. Corrigan, P. E. Dorey, R. Sasaki

    Pages 210-220

19. Contractions of quantum groups

    • E. Celeghini, R. Giachetti, E. Sorace, M. Tarlini

    Pages 221-244

20. New solutions of Yang-Baxter equations and quantum group structures

    • Mo-Lin Ge

    Pages 245-258

The theory of Quantum Groups is a rapidly developing area with numerous applications in mathematics and theoretical physics, e.g. in link and knot invariants in topology, q-special functions, conformal field theory, quantum integrable models. The aim of the Euler Institute's workshops was to review and compile the progress achieved in the different subfields. Near 100 participants came from 14 countries. More than 20 contributions written up for this book contain new, unpublished material and half of them include a survey of recent results in the field (deformation theory, graded differential algebras, contraction technique, knot invariants, q-special functions). FROM THE CONTENTS: V.G. Drinfeld: On Some Unsolved Problems in Quantum Group Theory.- M. Gerstenhaber, A. Giaquinto, S.D. Schack: Quantum Symmetry.- L.I. Korogodsky,L.L. Vaksman: Quantum G-Spaces and Heisenberg Algebra.-J. Stasheff: Differential Graded Lie Algebras, Quasi-Hopf Algebras and Higher Homotopy Algebras.- A.Yu. Alekseev, L.D. Faddeev, M.A. Semenov-Tian-Shansky: Hidden Quantum Groups inside Kac-Moody Algebras.- J.-L. Gervais: Quantum Group Symmetry of 2D Gravity.- T. Kohno: Invariants of 3-Manifolds Based on Conformal Field Theory and Heegaard Splitting.- O. Viro: Moves of Triangulations of a PL-Manifold.

• Quantum Algebras
• Quantum Groups
• Representation Theory
• Symmetries
• Theoretical physics
• Topology
• algebra

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