Petr P. Kulish – författare

The theory of Quantum Groups is a rapidly developing areawith numerous applications in mathematics and theoreticalphysics, e.g. in link and knot invariants in topology,q-special functions, conformal field theory, quantumintegrable models. The aim of the Euler Institute''sworkshops was to review and compile the progress achieved inthe different subfields. Near 100 participants came from 14countries. More than 20 contributions written up for thisbook contain new, unpublished material and half of theminclude a survey of recent results in the field (deformationtheory, graded differential algebras, contraction technique,knot invariants, q-special functions).FROM THE CONTENTS: V.G. Drinfeld: On Some Unsolved Problemsin 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-HopfAlgebras and Higher Homotopy Algebras.- A.Yu. Alekseev,L.D. Faddeev, M.A. Semenov-Tian-Shansky: Hidden QuantumGroups inside Kac-Moody Algebras.- J.-L. Gervais: QuantumGroup Symmetry of 2D Gravity.- T. Kohno: Invariants of3-Manifolds Based on Conformal Field Theory and HeegaardSplitting.- O. Viro: Moves of Triangulations of aPL-Manifold.

The theory of Quantum Groups is a rapidly developing areawith numerous applications in mathematics and theoreticalphysics, e.g. in link and knot invariants in topology,q-special functions, conformal field theory, quantumintegrable models. The aim of the Euler Institute'sworkshops was to review and compile the progress achieved inthe different subfields. Near 100 participants came from 14countries. More than 20 contributions written up for thisbook contain new, unpublished material and half of theminclude a survey of recent results in the field (deformationtheory, graded differential algebras, contraction technique,knot invariants, q-special functions).FROM THE CONTENTS: V.G. Drinfeld: On Some Unsolved Problemsin 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-HopfAlgebras and Higher Homotopy Algebras.- A.Yu. Alekseev,L.D. Faddeev, M.A. Semenov-Tian-Shansky: Hidden QuantumGroups inside Kac-Moody Algebras.- J.-L. Gervais: QuantumGroup Symmetry of 2D Gravity.- T. Kohno: Invariants of3-Manifolds Based on Conformal Field Theory and HeegaardSplitting.- O. Viro: Moves of Triangulations of aPL-Manifold.

This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems" held in July 2003 at the University of Algarve, Faro, Portugal, as a satellite workshop of the XIV International Congress on Mathematical Physics. In it, recent developments in the theory of infinite dimensional algebras, and their applications to quantum integrable systems, are reviewed by leading experts in the field.