The Geometry of Infinite-Dimensional GroupsThis 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
XII | 24 |
XIII | 26 |
XV | 29 |
XVI | 30 |
XVII | 35 |
XVIII | 38 |
XIX | 40 |
XX | 41 |
XXI | 42 |
XXII | 44 |
XXIII | 47 |
XXIV | 52 |
XXV | 58 |
XXVI | 65 |
XXVII | 67 |
XXIX | 70 |
XXX | 72 |
XXXI | 80 |
XXXII | 82 |
XXXIII | 86 |
XXXIV | 88 |
XXXVI | 90 |
XXXVII | 91 |
XXXVIII | 95 |
XXXIX | 99 |
XL | 105 |
XLI | 109 |
XLII | 111 |
XLIV | 113 |
XLV | 117 |
XLVI | 119 |
XLVII | 122 |
XLVIII | 124 |
XLIX | 129 |
L | 132 |
LI | 134 |
LIII | 136 |
LIV | 138 |
LV | 142 |
LVI | 146 |
LVII | 149 |
LXVII | 180 |
LXIX | 184 |
LXX | 187 |
LXXI | 189 |
LXXII | 192 |
LXXIII | 196 |
LXXIV | 197 |
LXXVI | 202 |
LXXVII | 206 |
LXXVIII | 209 |
LXXIX | 211 |
LXXX | 213 |
LXXXI | 215 |
LXXXII | 216 |
LXXXIII | 218 |
LXXXIV | 221 |
LXXXVI | 224 |
LXXXVII | 225 |
LXXXIX | 226 |
XC | 228 |
XCI | 231 |
XCII | 234 |
XCIII | 237 |
XCIV | 240 |
XCVI | 244 |
XCVII | 247 |
XCVIII | 250 |
XCIX | 252 |
C | 256 |
CI | 260 |
CIII | 263 |
CIV | 267 |
CVI | 268 |
CVII | 269 |
CVIII | 272 |
CX | 274 |
CXI | 277 |
| 281 | |
| 301 | |
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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
Bibliographic information
| Title | The 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 |
| Authors | Boris Khesin, Robert Wendt |
| Edition | illustrated |
| Publisher | Springer Science & Business Media, 2008 |
| ISBN | 3540772634, 9783540772637 |
| Length | 304 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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