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. |
Contents
Ludwig Faddeev and Alexander Volkov | 35 |
Jürg Fröhlich | 67 |
Simone Gutt and John Rawnsley | 103 |
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Deformation Theory and Symplectic Geometry Daniel Sternheimer,John Rawnsley,Simone Gutt No preview available - 2010 |
Common terms and phrases
Abelian action affine associative algebra automorphisms B₁ bundle C₁ canonical CH(X classical cochains coefficients commutative complex component connection construction corresponding curvature defined definition deformation quantization Deformation Theory denote diffeomorphisms differential graded Lie differential operators dimension dimensional element equation equivalence finite Flato formality conjecture formula g₁ given graded Lie algebra graph groupoid Hamiltonian Hochschild homology homotopy Hopf algebra infinitesimal integral invariant irreducible isomorphism Lagrangian lattice Lemma Lie group linear Math matrix module morphism multiplication Nambu noncommutative orbit parameter partition function Phys Poisson algebra Poisson bracket Poisson manifold polynomials proof Proposition quantum cohomology quantum groups R-matrix relation representation satisfy sinh Sp(V spectral star product Sternheimer subalgebra subgroup subset subspace symmetric Symplectic Geometry symplectic manifold tensor Theorem Toda lattice trivial vector fields vector space vertex operators Weyl zero πί