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.

Klappentext

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.

Inhalt

Preface. Noncommutative Differential Geometry and the Structure of Space Time; A. Connes. Shift Operator for the Discrete sl(2) Current Algebra; L. Faddeev, A. Volkov. Nambu Mechanics, n-ary Operations and their Quantization; M. Flato, et al. The Geometrization Principle; J. Fröhlich. Generalization and Deformations of Quantum Groups; C. Fronsdal. Quantized Intersection Cardinalities; M. Gerstenhaber. Deformation Quantization and Mpc Structures; S. Gutt, J. Rawnsley. Massless XXZ Model and Degeneration of the Elliptic Algebra Aq,p(sANDl2); M. Jimbo, et al. Formality Conjecture; M. Kontsevich. Quantum Cohomology of the Flag Manifold as an Algebra of Rational Functions on a Unipotent Algebraic Group; B. Kostant. Homologies Associated with Poisson Structures; O. Mathieu. Maximal Tori of Some Symplectomorphism Groups and Applications to Convexity; A. Bloch, et al. On 2D Yang-Mills Theory and Invariants of Links; M. Polyak, N. Reshetikhin. Some Applications of Quantum Shuffles; M. Rosso. Character Formulas and Localization of Integrals; W. Schmid. Deformation Theory and the Batalin-Vilkovisky Master Equation; J. Stasheff. The Fukaya Type Categories for Associative Algebras; R. Nest, B. Tsygan. Tangential Deformation Quantization and Polarized Symplectic Groupoids; A. Weinstein. Formal GNS Construction and WKB Expansion in Deformation Quantization; M. Bordemann, S. Waldmann. On the Deformation of Time Harmonic Flows; J. Hoppe. Distinguished Essential Extensions of Infinite Dimensional Classical Lie Algebras; A. Lichnerowicz. Noncommutative Contact Algebras; H. Omori, et al. Braided Geometry and the Inductive Construction of Lie Algebras and Quantum Groups; S. Majid. Star Products in the Triangular Case; C. Moreno, L. Valero. Aspetti fisici della teoria delle deformazioni; G. Dito. Scientific Programme. List of Participants.