The Geometry of Infinite-Dimensional Groups

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Springer Science & Business Media, Sep 28, 2008 - Mathematics - 304 pages
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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 geometry. The text includes many exercises and open questions.

 

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Contents

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Copyright

Other editions - View all

The Geometry of Infinite-Dimensional Groups
Boris Khesin,Robert Wendt
No preview available - 2009
The Geometry of Infinite-Dimensional Groups
Boris Khesin,Robert Wendt
No preview available - 2009

Common terms and phrases

2-cocycle abelian adjoint algebra g analogue bilinear form boundary Calogero–Moser system central extension Chern–Simons circle coadjoint action coadjoint orbits coadjoint representation cocycle codimension commutator compact conjugacy classes conjugate consider defined Definition denote derivative Diff(M different differential operators dimension divisor dual space element elliptic curve elliptic Lie Euler equation Exercise exponential map finite first fixed flat connections flow fluid formula G-bundle gauge transformations geodesic Gint given Hamiltonian function hence HoLG holomorphic hyperplane infinite infinite-dimensional Lie integral invariant isomorphic Lie bracket Lie group G linear linking number loop algebra loop group matrix meromorphic metric moduli space moment map monodromy pairing Poisson bracket Poisson structure polar homology Proof Proposition quadratic quotient Remark Riemann surface Riemannian root system SDiff(M subalgebra subgroup submanifold symplectic structure tangent space Theorem torus Vect(M vector bundle vector fields vector space zero

About the author (2008)

B.Khesin's areas of research are infinite-dimensional Lie groups, integrable systems, Poisson geometry, and topological hydrodynamics. Together with Vladimir Arnold he is the author of the monograph on "Topological methods in hydrodynamics", which has become a standard reference in mathematical fluid dynamics. He was a Sloan research fellow in 1997-1999 and a Clay Mathematics Institute book fellow in 2006-2007, as well as an Andre-Aizenstadt prize recepient in 1998.

R.Wendt's fields of research include the geometry and representation theory of infinite dimensional Lie groups and algebras, related geometric structures, and mathematical physics. He is also interested in mathematical finance and 'real world' applications of financial modelling

Bibliographic information

QR code for The Geometry of Infinite-Dimensional Groups
TitleThe Geometry of Infinite-Dimensional Groups
A series of modern surveys in mathematics
Volume 51 of Ergebnisse der Mathematik und ihrer Grenzgebiete : a series of modern surveys in mathematics. Folge 3
Ergebnisse der Mathematik und ihrer Grenzgebiete
AuthorsBoris Khesin, Robert Wendt
Editionillustrated
PublisherSpringer Science & Business Media, 2008
ISBN3540772634, 9783540772637
Length304 pages
Subjects ›  › 

Mathematics / Algebra / Abstract
Mathematics / Algebra / General
Mathematics / Geometry / Algebraic
Mathematics / Geometry / General
Mathematics / Group Theory
Mathematics / Mathematical Analysis
Mathematics / Numerical Analysis
Science / Physics / Mathematical & Computational
  
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