## Deformation Theory and Symplectic GeometryDaniel Sternheimer, John Rawnsley, Simone Gutt This volume contains papers presented at the meeting Deformation Theory, Symplectic Geometry and Applications, held in Ascona, June 17-21, 1996. The contents touch upon many frontier domains of modern mathematics, mathematical physics and theoretical physics and include authoritative, state-of-the-art contributions by leading scientists. New and important developments in the fields of symplectic geometry, deformation quantization, noncommutative geometry (NCG) and Lie theory are presented. Among the subjects treated are: quantization of general Poisson manifolds; new deformations needed for the quantization of Nambu mechanics; quantization of intersection cardinalities; quantum shuffles; new types of quantum groups and applications; quantum cohomology; strong homotopy Lie algebras; finite- and infinite-dimensional Lie groups; and 2D field theories and applications of NCG to gravity coupled with the standard model. Audience: This book will be of interest to researchers and post-graduate students of mathematical physics, global analysis, analysis on manifolds, topological groups, nonassociative rings and algebras, and Lie algebras. |

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### Contents

Ludwig Faddeev and Alexander Volkov | 35 |

Jiirg Frohlich | 67 |

Murray Gerstenhaber | 85 |

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### Common terms and phrases

Abelian action affine associative algebra automorphisms basis bundle canonical CH(XV CH{Xy classical cochains coefficients commutative complex component connection consider construction corresponding curvature defined definition deformation quantization Deformation Theory denote diffeomorphisms differential graded Lie differential operators dimension dimensional eigenvalues element equation equivalence finite Flato formality conjecture formula Gerstenhaber given graded Lie algebra graph groupoid Hamiltonian Hochschild homology homotopy Hopf algebra identity infinitesimal integral invariant irreducible isomorphism Kac-Moody algebras Lagrangian lattice Lemma Lie group linear Math Mathematics matrix module morphism Moyal multiplication Nambu bracket noncommutative orbit orthogonal parameter partition function Phys Poisson algebra Poisson bracket Poisson manifold polynomials proof Proposition quantum cohomology quantum groups R-matrix representation satisfy sinh spectral standard R-matrix star product Sternheimer subalgebra subgroup subsets subspace symmetric Symplectic Geometry symplectic manifold tensor Theorem trivial usual product vector fields vector space Weyl Yang-Baxter relation