000 | 04018nam a22005777a 4500 | ||
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001 | sulb-eb0023904 | ||
003 | BD-SySUS | ||
005 | 20160413122414.0 | ||
007 | cr nn 008mamaa | ||
008 | 120824s2013 gw | s |||| 0|eng d | ||
020 |
_a9783642310904 _9978-3-642-31090-4 |
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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, 464 p. _bonline resource. |
||
336 |
_atext _btxt _2rdacontent |
||
337 |
_acomputer _bc _2rdamedia |
||
338 |
_aonline resource _bcr _2rdacarrier |
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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 | _aNonassociative rings. | |
650 | 0 | _aRings (Algebra). | |
650 | 0 | _aTopological groups. | |
650 | 0 | _aLie groups. | |
650 | 0 | _aMathematical analysis. | |
650 | 0 | _aAnalysis (Mathematics). | |
650 | 0 | _aDifferential 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 | ||
942 |
_2Dewey Decimal Classification _ceBooks |
||
999 |
_c45996 _d45996 |