By V. G. Drinfeld (auth.), Petr P. Kulish (eds.)
The conception of Quantum teams is a speedily constructing zone with a number of functions in arithmetic and theoretical physics, e.g. in hyperlink and knot invariants in topology, q-special services, conformal box idea, quantum integrable versions. the purpose of the Euler Institute's workshops used to be to check and collect the growth accomplished within the assorted subfields. close to a hundred contributors got here from 14 nations. greater than 20 contributions written up for this booklet include new, unpublished fabric and 1/2 them comprise a survey of modern ends up in the sphere (deformation concept, graded differential algebras, contraction process, knot invariants, q-special functions). FROM THE CONTENTS: V.G. Drinfeld: On a few Unsolved difficulties in Quantum workforce 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 better Homotopy Algebras.- A.Yu. Alekseev, L.D. Faddeev, M.A. Semenov-Tian-Shansky: Hidden Quantum teams inside of Kac-Moody Algebras.- J.-L. Gervais: Quantum workforce Symmetry of second Gravity.- T. Kohno: Invariants of 3-Manifolds in accordance with Conformal box conception and Heegaard Splitting.- O. Viro: strikes of Triangulations of a PL-Manifold.