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" Higher structures in geometry and physics : "
Alberto S. Cattaneo, Anthony Giaquinto, Ping Xu, editors
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BL
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| Record Number
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598959
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b428178
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| Title & Author
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Higher structures in geometry and physics : : in honor of Murray Gerstenhaber and Jim Stasheff /\ Alberto S. Cattaneo, Anthony Giaquinto, Ping Xu, editors
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| Series Statement
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Progress in mathematics ;; v. 287
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| Page. NO
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1 online resource (xv, 362 pages) :: color portraits
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| ISBN
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9780817647353
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: 081764735X
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: 9780817647346
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: 0817647341
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| Bibliographies/Indexes
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Includes bibliographical references
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| Contents
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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 Space-Time 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
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Twisting Elements in Homotopy G-AlgebrasHomological 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 bi-quantification à la théorie de Lie; Higher Homotopy Hopf Algebras Found: A Ten-Year Retrospective
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| Abstract
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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
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| Subject
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Algebra
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Mathematics
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| Dewey Classification
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512
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| LC Classification
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QA154.3.H54 2011
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| Added Entry
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Cattaneo, A. S., (Alberto S.)
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Giaquinto, Anthony
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Xu, Ping
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