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＜電子ブック＞
The Geometry of Infinite-Dimensional Groups / by Boris Khesin, Robert Wendt

版	1st ed. 2009.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2009
本文言語	英語
大きさ	XII, 304 p : online resource
著者標目	*Khesin, Boris author Wendt, Robert author SpringerLink (Online service)
件　名	LCSH:Topological groups LCSH:Lie groups LCSH:Group theory LCSH:Geometry LCSH:Mathematical physics LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Algebraic geometry FREE:Topological Groups and Lie Groups FREE:Group Theory and Generalizations FREE:Geometry FREE:Mathematical Methods in Physics FREE:Global Analysis and Analysis on Manifolds FREE:Algebraic Geometry
一般注記	Preface -- Introduction -- I Preliminaries -- II Infinite-dimensional Lie Groups: Their Geometry, Orbits and Dynamical Systems -- III Applications of Groups: Topological and Holomorphic Gauge Theories -- Appendices -- A1 Root Systems -- A2 Compact Lie Groups -- A3 Krichever-Novikov Algebras -- A4 Kähler Structures on the Virasoro and Loop Group Coadjoint Orbits -- A5 Metrics and Diameters of the Group of Hamiltonian Diffeomorphisms -- A6 Semi-Direct Extensions of the Diffeomorphism Group and Gas Dynamics -- A7 The Drinfeld-Sokolov Reduction -- A8 Surjectivity of the Exponential Map on Pseudo-Differential Symbols -- A9 Torus Actions on the Moduli Space of Flat Connections -- Bibliography -- Index This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. While infinite-dimensional groups often exhibit very peculiar features, this book describes unifying geometric ideas of the theory and gives numerous illustrations and examples, ranging from the classification of the Virasoro coadjoint orbits to knot theory, from optimal mass transport to moduli spaces of flat connections on surfaces. The text includes many exercises and open questions, and it is accessible to both students and researchers in Lie theory, geometry, and Hamiltonian systems HTTP:URL=https://doi.org/10.1007/978-3-540-77263-7

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