000 03879nam a22005295i 4500
001 978-3-642-31090-4
003 DE-He213
005 20140220082849.0
007 cr nn 008mamaa
008 120824s2013 gw | s |||| 0|eng d
020 _a9783642310904
_9978-3-642-31090-4
024 7 _a10.1007/978-3-642-31090-4
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515
_223
100 1 _aLaurent-Gengoux, Camille.
_eauthor.
245 1 0 _aPoisson Structures
_h[electronic resource] /
_cby Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aXXIV, 461 p. 16 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v347
505 0 _aPart I Theoretical Background:1.Poisson Structures: Basic Definitions -- 2.Poisson Structures: Basic Constructions -- 3.Multi-Derivations and Kähler Forms -- 4.Poisson (Co)Homology -- 5.Reduction -- Part II Examples:6.Constant Poisson Structures, Regular and Symplectic Manifolds -- 7.Linear Poisson Structures and Lie Algebras -- 8.Higher Degree Poisson Structures -- 9.Poisson Structures in Dimensions Two and Three -- 10.R-Brackets and r-Brackets -- 11.Poisson–Lie Groups -- Part III Applications:12.Liouville Integrable Systems -- 13.Deformation Quantization -- A Multilinear Algebra -- B Real and Complex Differential Geometry -- References -- Index -- List of Notations.  .
520 _aPoisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aTopological Groups.
650 0 _aGlobal analysis (Mathematics).
650 0 _aGlobal differential geometry.
650 1 4 _aMathematics.
650 2 4 _aAnalysis.
650 2 4 _aDifferential Geometry.
650 2 4 _aTopological Groups, Lie Groups.
650 2 4 _aNon-associative Rings and Algebras.
700 1 _aPichereau, Anne.
_eauthor.
700 1 _aVanhaecke, Pol.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642310898
830 0 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v347
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-31090-4
912 _aZDB-2-SMA
999 _c97062
_d97062