The Geometry of Infinite-Dimensional Groups

• Κύριοι συγγραφείς: Khesin, Boris (Συγγραφέας), Wendt, Robert (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Σειρά: Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics ; 51
• Θέματα: Mathematics.; Algebraic geometry.; Group theory.; Topological groups.; Lie groups.; Global analysis (Mathematics).; Manifolds (Mathematics).; Geometry.; Physics.; Topological Groups, Lie Groups.; Group Theory and Generalizations.; Mathematical Methods in Physics.; Global Analysis and Analysis on Manifolds.; Algebraic Geometry.

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...

Πίνακας περιεχομένων:

• 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.