Deformation Theory and Symplectic Geometry

by Sternheimer, Daniel; Rawnsley, John; Gutt, Simone

• ISBN13: 9780792345251
• ISBN10: 0792345258
• Format: Hardcover
• Copyright: 1997-06-01
• Publisher: Kluwer Academic Pub

Summary

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.

Table of Contents

Preface	vii
Alain Connes
Noncommutative Differential Geometry and the Structure of Space Time	1	(34)
Ludwig Faddeev
Alexander Volkov
Shift operator for the discrete sl(2) current algebra	35	(8)
Moshe Flato
Giuseppe Dito
Daniel Sternheimer
Nambu mechanics, n-ary operations and their quantization	43	(24)
Jurg Frohlich
The Geometrization Principle	67	(2)
Christian Fronsdal
Generalization and deformations of quantum groups	69	(16)
Murray Gerstenhaber
Quantized intersection cardinalities	85	(18)
Simone Gutt
John Rawnsley
Deformation quantization and Mp(c) structures	103	(14)
Michio Jimbo
Hitoshi Konno
Tetsuji Miwa
Massless X X Z model and degeneration of the elliptic algebra A(q,p) (sl(2))	117	(22)
Maxim Kontsevich
Formality conjecture	139	(18)
Bertram Kostant
Quantum cohomology of the flag manifold as an algebra of rational functions on a unipotent algebraic group	157	(20)
Olivier Mathieu
Homologies associated with Poisson structures	177	(24)
Anthony Bloch
Mohamed Ould El Hadrami
Hermann Flaschka
Tudor S. Ratiu
Maximal tori of some symplectomorphism groups and applications to convexity	201	(22)
Michael Polyak
Nicolai Reshetikhin
On 2D Yang-Mills theory and invariants of links	223	(26)
Marc Rosso
Some applications of quantum shuffles	249	(10)
Wilfried Schmid
Character formulas and localization of integrals	259	(12)
Jim Stasheff
Deformation theory and the Batalin-Vilkovisky Master Equation	271	(14)
Ryszard Nest
Boris Tsygan
The Fukaya type categories for associative algebras	285	(16)
Alan Weinstein
Tangential deformation quantization and polarized symplectic groupoids	301	(14)
Martin Bordemann
Stefan Waldmann
Formal GNS construction and WKB expansion in deformation quantization	315	(6)
Jens Hoppe
On the deformation of time harmonic flows	321	(6)
Andre Lichnerowicz
Distinguished essential extensions of infinite dimensional classical Lie algebras	327	(6)
Hideki Omori
Yoshiaki Maeda
Naoya Miyazaki
Akira Yoshioka
Noncommutative contact algebras	333	(6)
Shahn Majid
Braided geometry and the inductive construction of Lie algebras and quantum groups	339	(6)
Carlos Moreno
Luis Valero
Star products in the triangular case	345	(8)
Giuseppe Dito
Aspetti fisici della teoria delle deformazioni	353	(2)
Scientific programme	355	(3)
List of participants	358