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001 978-0-8176-4735-3
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005 20140220083711.0
007 cr nn 008mamaa
008 101125s2011 xxu| s |||| 0|eng d
020 _a9780817647353
_9978-0-8176-4735-3
024 7 _a10.1007/978-0-8176-4735-3
_2doi
050 4 _aQA252.3
050 4 _aQA387
072 7 _aPBG
_2bicssc
072 7 _aMAT014000
_2bisacsh
072 7 _aMAT038000
_2bisacsh
082 0 4 _a512.55
_223
082 0 4 _a512.482
_223
100 1 _aCattaneo, Alberto S.
_eeditor.
245 1 0 _aHigher Structures in Geometry and Physics
_h[electronic resource] :
_bIn Honor of Murray Gerstenhaber and Jim Stasheff /
_cedited by Alberto S. Cattaneo, Anthony Giaquinto, Ping Xu.
264 1 _aBoston :
_bBirkhäuser Boston,
_c2011.
300 _aXV, 362p. 92 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Mathematics ;
_v287
505 0 _aTopics 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.
520 _aThis 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.
650 0 _aMathematics.
650 0 _aGeometry, algebraic.
650 0 _aGroup theory.
650 0 _aTopological Groups.
650 0 _aMathematical physics.
650 1 4 _aMathematics.
650 2 4 _aTopological Groups, Lie Groups.
650 2 4 _aGroup Theory and Generalizations.
650 2 4 _aAlgebraic Geometry.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aApplications of Mathematics.
700 1 _aGiaquinto, Anthony.
_eeditor.
700 1 _aXu, Ping.
_eeditor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817647346
830 0 _aProgress in Mathematics ;
_v287
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-8176-4735-3
912 _aZDB-2-SMA
999 _c105081
_d105081