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The geometry of infinite dimensional groups

Author: Boris A Khesin; Robert Wendt
Publisher: Berlin : Springer, 2009.
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete., 3. Folge,, 3. Folge ;, 51
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
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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  Read more...

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Document Type: Book
All Authors / Contributors: Boris A Khesin; Robert Wendt
ISBN: 9783540772620 3540772626
OCLC Number: 474253388
Notes: Literaturangaben.
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 Kahler 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.
Description: xii, 304 S. : ill. ; 24 cm.
Contents: Preliminaries.- Infinite-Dimensional Lie Groups: Their Geometry, Orbits, and Dynamical Systems.- Applications of Groups: Topological and Holomorphic Gauge Theories.
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete., 3. Folge,, 3. Folge ;, 51
Responsibility: Boris Khesin, Robert Wendt.
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From the reviews: "The book under review is a welcome addition to the literature on infinite-dimensional Lie groups. ... the present monograph is to 'present the unifying ideas of the theory by Read more...

 
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