Series 
Progress in mathematics ; v. 287 

Progress in mathematics (Boston, Mass.) ;
v. 287.

Subject 
Algebra.

Alt Name 
Cattaneo, A. S. (Alberto S.)


Giaquinto, Anthony.


Xu, Ping, Professor.

Description 
1 online resource (xv, 362 pages) : color portraits. 
Note 
Articles in English and French. 
Bibliography Note 
Includes bibliographical references. 
Contents 
Higher Structures in Geometry and Physics; Foreword; Preface; Contents; List of Contributors; Topics in Algebraic Deformation Theory; Origins and Breadth of the Theory of Higher Homotopies; The Deformation Philosophy, Quantization and Noncommutative SpaceTime Structures; Differential Geometry of Gerbes and Differential Forms; Symplectic Connections of Ricci Type and Star Products; Effective Batalin  Vilkovisky Theories, Equivariant Configuration Spaces and Cyclic Chains; Noncommutative Calculus and the Gauss  Manin Connection; The Lie Algebra Perturbation Lemma. 

Twisting Elements in Homotopy GAlgebrasHomological Perturbation Theory and Homological Mirror Symmetry; Categorification of Acyclic Cluster Algebras: An Introduction; Poisson and Symplectic Functions in Lie Algebroid Theory; The Diagonal of the Stasheff Polytope; Permutahedra, HKR Isomorphism and Polydifferential Gerstenhaber  Schack Complex; Applications de la biquantification a la theorie de Lie; Higher Homotopy Hopf Algebras Found: A TenYear Retrospective. 
Summary 
This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. Each contribution in this volume expands on the ideas of. 
Note 
Print version record. 
ISBN 
9780817647353 (electronic bk.) 

081764735X (electronic bk.) 

9780817647346 (electronic bk.) 

0817647341 (electronic bk.) 
ISBN/ISSN 
10.1007/9780817647353 
OCLC # 
695389131 
Additional Format 
Print version: Higher structures in geometry and physics. [New York?] : Birkhauser, 2011 9780817647346 (OCoLC)698163956 
