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＜電子ブック＞
Higher Structures in Geometry and Physics : In Honor of Murray Gerstenhaber and Jim Stasheff / edited by Alberto S. Cattaneo, Anthony Giaquinto, Ping Xu
(Progress in Mathematics. ISSN:2296505X ; 287)

版	1st ed. 2011.
出版者	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
出版年	2011
大きさ	XV, 362 p. 92 illus : online resource
著者標目	Cattaneo, Alberto S editor Giaquinto, Anthony editor Xu, Ping editor SpringerLink (Online service)
件　名	LCSH:Topological groups LCSH:Lie groups LCSH:Group theory LCSH:Algebraic geometry LCSH:Mathematical physics LCSH:Mathematics FREE:Topological Groups and Lie Groups FREE:Group Theory and Generalizations FREE:Algebraic Geometry FREE:Mathematical Methods in Physics FREE:Applications of Mathematics
一般注記	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 -- Twisting Elements in Homotopy G-algebras -- Homological 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 a la théorie de Lie -- Higher homotopy Hopf algebras found: A ten year retrospective 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. The ideas of higher homotopies and algebraic deformation have a growing number of theoretical applications and have played a prominent role in recent mathematical advances. For example, algebraic versions of higher homotopies have led eventually to the proof of the formality conjecture and the deformation quantization of Poisson manifolds. As observed in deformations and deformation philosophy, a basic observation is that higher homotopy structures behave much better than strict structures. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. Higher Structures in Geometry and Physics is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures. Contributors: L. Breen, A.S. Cattaneo, M. Cahen, V.A. Dolgushev, G. Felder, A. Giaquinto, S. Gutt, J. Huebschmann, T. Kadeishvili, H. Kajiura, B. Keller, Y. Kosmann-Schwarzbach, J.-L. Loday, S.A. Merkulov, D. Sternheimer, D.E. Tamarkin, C. Torossian, B.L. Tsygan, S. Waldmann, R.N. Umble HTTP:URL=https://doi.org/10.1007/978-0-8176-4735-3

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