The Geometry of Infinite-Dimensional Groups

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Khesin, Boris (Autor), Wendt, Robert (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2009.
Edición:1st ed. 2009.
Temas:
Topological groups.
Lie groups.
Group theory.
Geometry.
Mathematical physics.
Global analysis (Mathematics).
Manifolds (Mathematics).
Algebraic geometry.
Topological Groups and Lie Groups.
Group Theory and Generalizations.
Mathematical Methods in Physics.
Global Analysis and Analysis on Manifolds.
Algebraic Geometry.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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