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Deformation Theory and Symplectic Geometry : Mathematical Physics Studies - Daniel Sternheimer

Deformation Theory and Symplectic Geometry

Mathematical Physics Studies

By: Daniel Sternheimer (Editor)

Hardcover Published: 31st July 1997
ISBN: 9780792345251
Number Of Pages: 368

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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.

Noncommutative Differential Geometry and the Structure of Space Timep. 1
Shift operator for the discrete sl(2) current algebrap. 35
Nambu mechanics, n-ary operations and their quantizationp. 43
The Geometrization Principlep. 67
Generalization and deformations of quantum groupsp. 69
Quantized intersection cardinalitiesp. 85
Deformation quantization and M p[superscript c] structuresp. 103
Massless XXZ model and degeneration of the elliptic algebra A[subscript q,p](sl[subscript 2])p. 117
Formality conjecturep. 139
Quantum cohomology of the flag manifold as an algebra of rational functions on a unipotent algebraic groupp. 157
Homologies associated with Poisson structuresp. 177
Maximal tori of some symplectomorphism groups and applications to convexityp. 201
On 2D Yang-Mills theory and invariants of linksp. 223
Some applications of quantum shufflesp. 249
Character formulas and localization of integralsp. 259
Deformation theory and the Batalin-Vilkovisky Master Equationp. 271
The Fukaya type categories for associative algebrasp. 285
Tangential deformation quantization and polarized symplectic groupoidsp. 301
Formal GNS construction and WKB expansion in deformation quantizationp. 315
On the deformation of time harmonic flowsp. 321
Distinguished essential extensions of infinite dimensional classical Lie algebrasp. 327
Noncommulative contact algebrasp. 333
Braided geometry and the inductive construction of Lie algebras and quantum groupsp. 339
Star products in the triangular casep. 345
Aspetti fisici della teoria delle deformazionip. 353
Scientific programmep. 355
List of participantsp. 358
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792345251
ISBN-10: 0792345258
Series: Mathematical Physics Studies
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 368
Published: 31st July 1997
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 2.24
Weight (kg): 0.72