LEADER 05363nam 2200601 450 001 996466619403316 005 20220908100308.0 010 $a3-540-47020-4 024 7 $a10.1007/BFb0101174 035 $a(CKB)1000000000437109 035 $a(SSID)ssj0000326041 035 $a(PQKBManifestationID)12081456 035 $a(PQKBTitleCode)TC0000326041 035 $a(PQKBWorkID)10265894 035 $a(PQKB)11771184 035 $a(DE-He213)978-3-540-47020-5 035 $a(MiAaPQ)EBC5578781 035 $a(Au-PeEL)EBL5578781 035 $a(OCoLC)1066183772 035 $a(MiAaPQ)EBC6842343 035 $a(Au-PeEL)EBL6842343 035 $a(PPN)155216333 035 $a(EXLCZ)991000000000437109 100 $a20220908d1992 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 00$aQuantum groups $eproceedings of workshops held in the Euler International Mathematical Institute, Leningrad, Fall 1990 /$fP. P. Kulish, editor 205 $a1st ed. 1992. 210 1$aBerlin ;$aHeidelberg :$cSpringer-Verlag,$d[1992] 210 4$dİ1992 215 $a1 online resource (XII, 408 p.) 225 1 $aLecture Notes in Mathematics ;$vVolume 1510 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-55305-3 327 $aOn some unsolved problems in quantum group theory -- Quantum symmetry -- Yang-Baxter equation and deformation of associative and Lie algebras -- Quantum G-spaces and Heisenberg algebra -- Real and imaginary forms of quantum groups -- Rank of quantum groups and braided groups in dual form -- Yangians of the ?strange? lie superalgebras -- Askey-wilson polynomials as spherical functions on SU q(2) -- Twisted yangians and infinite-dimensional classical Lie algebras -- Differential graded Lie algebras, quasi-hopf algebras and higher homotopy algebras -- Quantum deformation of the flag variety -- Zonal spherical functions on quantum symmetric spaces and MacDonald's symmetric polynomials -- Hidden quantum groups inside Kac-Moody algebras -- Liouville theory on the lattice and universal exchange algebra for bloch waves -- Non-local currents in 2D QFT: An alternative to the quantum inverse scattering method -- Induced representations and tensor operators for quantum groups -- Affine toda field theory: S-matrix vs perturbation -- Contractions of quantum groups -- New solutions of Yang-Baxter equations and quantum group structures -- Quantum group symmetry of 2D gravity -- Extended chiral conformal theories with a quantum symmetry -- Fusion rsos models and rational coset models -- Integrable time-discrete systems: Lattices and mappings -- On relations between poisson groups and quantum groups -- Characters of Hecke and Birman-Wenzl algebras -- Invariants of 3-Manifolds based on conformal field theory and Heegaard splitting -- The multi-variable alexander polynomial and a one?parameter family of representations of U q (sl(2,C)) at q 2=?1 -- Preparation theorems for isotopy invariants of links in 3-manifolds -- Quantum invariants of 3-manifold and a glimpse of shadow topology -- Moves of triangulations of a PL-manifold -- Yang-Baxter relation, exactly solvable models and link polynomials -- Triangularity of transition matrices for generalized Hall-Littlewood polynomials -- An open problem in quantum groups -- Two problems in quantized algebras of functions -- Unsolved problems -- On classification of ?-graded Lie algebras of constant growth which have algebra ?[h] as Cartan subalgebra. 330 $aThe theory of Quantum Groups is a rapidly developing area with numerous applications in mathematics and theoretical physics, e.g. in link and knot invariants in topology, q-special functions, conformal field theory, quantum integrable models. The aim of the Euler Institute's workshops was to review and compile the progress achieved in the different subfields. Near 100 participants came from 14 countries. More than 20 contributions written up for this book contain new, unpublished material and half of them include a survey of recent results in the field (deformation theory, graded differential algebras, contraction technique, knot invariants, q-special functions). FROM THE CONTENTS: V.G. Drinfeld: On Some Unsolved Problems in Quantum Group Theory.- M. Gerstenhaber, A. Giaquinto, S.D. Schack: Quantum Symmetry.- L.I. Korogodsky,L.L. Vaksman: Quantum G-Spaces and Heisenberg Algebra.-J. Stasheff: Differential Graded Lie Algebras, Quasi-Hopf Algebras and Higher Homotopy Algebras.- A.Yu. Alekseev, L.D. Faddeev, M.A. Semenov-Tian-Shansky: Hidden Quantum Groups inside Kac-Moody Algebras.- J.-L. Gervais: Quantum Group Symmetry of 2D Gravity.- T. Kohno: Invariants of 3-Manifolds Based on Conformal Field Theory and Heegaard Splitting.- O. Viro: Moves of Triangulations of a PL-Manifold. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$vVolume 1510. 606 $aConformal invariants$vCongresses 606 $aQuantum field theory$vCongresses 615 0$aConformal invariants 615 0$aQuantum field theory 676 $a512.55 702 $aKulish$b P. P$g(Petr P.),$f1944- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466619403316 996 $aQuantum groups$980126 997 $aUNISA