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Rosenfeld B. — Geometry of Lie Groups
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Название: Geometry of Lie GroupsАвтор: Rosenfeld B. Аннотация: This book represents the fruits of the author's many years of research and teaching. The introductory chapter contains the necessary background information from algebra, topology, and geometry of real spaces. Chapter 1 presents more specialized information on associative and nonassociative algebras and on Lie groups and algebras. In Chapters 2 through 6 geometric interpretations of all simple Lie groups of classes An, Bn, Cn, and Dn as well as of finite groups of Lie type are given. In Chapters 5 and 6 geometric interpretations of quasisimple and r-quasisimple Lie groups of the same classes are included. In Chapter 7, for the first time ever, geometric interpretations of all simple and quasisimple Lie groups of exceptional classes G2, F4, E6, E7, and E8 are given. The role of exercises is played by the assertions and theorems given without a full proof, but with the indication that they can be proved analogously to already proved theorems. Audience: The book will be of interest to graduate students and researchers in mathematics and physics.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1997Количество страниц: 393Добавлена в каталог: 18.10.2010Операции: Положить на полку |
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Inertia 329 Inner product 8 Interior 5 Interior of an oval hyperquadric 220 Interior, domain of a hypersphere 10 388 Interpretation of Hermitian hyperbolic space in Euclidean space 234 Interpretation of manifolds of lines 3—planes 236 Interpretation of quadratic space by hyperspheres 238 Interpretation of quasisymplectic spaces 314—315 Interpretation of quaternionic symplectic space 318—320 Interpretation of real symplectic space 315—316 Intersection 7 Invariance axiom 197 Invariant subgroup 3 Invariants of equations of hyperquadrics 187—188 Invariants of two points in a quaternionic symplectic space 314 Inversion in hypercycle 299 Inversion in hyperquadric 143 Inversion in hypersphere 11 Inversive space 11 Irreducible linear representation of a group 93 Isoclinic m-planes 179 Isomorphism 2 Isomorphisms of simple Lie groups 69 82 Isotropic space 288 Iwasawa decomposition 256 Jacobi identity 23 Jacobsons theorems 89 Jordan, algebra, commutative 87 Jordan, general 91 Jordan, ternar 92 Kahlerian manifold 326 Kantor theorems 101—104 Kantor — Koecher theorem 104 Karpova theorem 308 Khayyam — Saccheri quadrangle 262—263 Killing-Cartan, form 25 Killing-Cartan, theorem 64 Kinematical twist 201 Klein bottle 279—280 Kleinian group 268 Klimanova — Petsko theorem 307 Kneser theorem 196—197 Kolmogorov axioms 120 Kotelnikov — Study — Fubini interpretations 235 Kronecker product 96 Lagrangean n-plane 313 Lanner group 268—270 Latitude 193 Lattice 6 Lie, algebra 23 Lie, group 21 Lie, ternar 92 Liebmann theorem 257 Light quadruple, tetrad 218 Limit point 5 Line (straight) 7 Linear, complex of lines 152 Linear, congruence of lines 112 Linear, dependence, independence of vectors 4 Linear, operator 13 Linear, representation of a group 93 Linear, space 3 Linear, transformation 4 12 Linnik theorem 40 56 Liouville theorem 204 Lipschitz theorem 97 Lipschitzian 98 151 Local absolute, superabsolute of a symmetric space 269—276 354—356 Locally isomorphic Lie groups 21 longitude 193 Loop 2 Lorentz transformation 216 m — Pair 132 m — Planar apex of a hypercone 148 m — Planar generators 143 m — Plane 7 114 m — Simplex 184 m — Sphere 11 211 Magma 2 Main moment in elliptic of a system of sliding vectors 199 203 Main moment in elliptic, hyperbolic space 281 Manifold of generators of maximal dimension of real hyperquadric 259—260 Manifold of m-planar generators of a hyperquadric 144—145 150—151 164-165 Mathieu groups, planes 214 Matrix 40 Matrix, coordinates, affine 133—134 Matrix, equidistant hyperquadric 252 Matrix, projective, tangential 129 771 Meridian 193 Metasymplectic geometries 351 Metric of spherical sliding vector 202 Metric, automorphism 33 Metric, face 184 Metric, hyperquadric, linear complex 304 Metric, m-horosphere 305 Metric, space 8 Metric, tensor 15 771 Miquel theorems 207—208 Mobius strip 170 279—280 Modular group 268 Module 106 Modulus 8 29—31 35 40 43 46 49 51 55 56 Molien, criterion 37 Molien, theorem 45 Moment of couple of vectors 199 Monoid 2 Motion 25 175 227 336 Multiple number 35 n — Chain 157 n — Cocube 184 n — Cube 184 Nabla operator 14 Natural topology 10 Neighborhood 5 Nonsingular matrix 41 Normal, 2-bichains 333 348 Normal, n-chains 182 269 337 342—343 347—348 Normal, vector 12 Null lines 153 Null points 154 Null-system 153 166 Octave, octonion 54 Octonionic symplectic 5-space 350 Octooctonion 60 Octooctonionic Hermitian plane 344—348 One-element extension 214 Operators of complex, split complex, dual structure 107 Orbit 25 Ordered set 6 Oriented volume 184 Origin 7 Orthogonal group 22 Orthogonality 9 Oval hyperquadric 147 Pappus, configuration 155 Pappus, theorem 109 119 Parabolic, common perpendiculars of ma-planes 301 Parabolic, figure 102 Parabolic, lines of kind a 299 Parabolic, space 102 Parabolic, subalgebra, subgroup 101 Paraboloid 140 Parallel, displacement 16 Parallel, m-planes 7 Parallelepiped, parallelogram 184 Parallels 194 Parameter of a m-equidistant hyperquadric 253 Paratactic, congruence of lines 230 304 7 Paratactic, m-planes 229 301 Partially ordered set 6 Pascal theorem 120 Pentaspherical coordinates 206 Petsko interpretation 240 Plane 7 114 Pluecker, coordinates 103 Pluecker, interpretation 121 239 Plural number 35 Poincare, interpretation 232 Poincare, polynomial 85 Poincare, transformation 216 Point at infinity 7 11 114 Point of reference of main moment 199 Point, apex of a hypercone 140 390 Polar, conjugate points 141 147 Polar, great circle 191 Polar, hyperplane 141 Polar, triangle 191 Polarized parabolic p-plane 304 Pole 141 Polygon 184 Polyhedron 184 Polynomial algebra 36 Polytope 184 Pontryagin theorems 40 55 Popovic interpretation 264 Position vector 7 114 Positivity axiom 8 197 Primitive group 25 Principal, axes of a hyperquadric 186 Principal, axis of a system of sliding vectors 200 Projective, configuration 155 Projective, coordinates 114 Projective, space 7 Projective, transformation 27 Prvanovic theorem 248 Pseudo — Clifford number 51 Pseudo — Euclidean space 10 168 Pseudo — Galilean space 288 Pseudo — Kahlerian manifold 326 Pseudo — Riemannian manifold 15 Pseudoaltemion 51 Pseudoconformal space 11 209 Pseudoelliptic space 219 223 Pseudohyperbolic space 219 223 Pseudoisotropic space 288 Pseudometric space 8 Pseudoorthogonal group 22 Quarter-octonion 60 Quartic curve with 28 Quartic curve with double tangents 72 151 Quasi — Cartan algorithm 289 Quasi — Euclidean space 288 Quasi — Lanner group 268—269 271—274 Quasi — Riemannian manifold 307 Quasialternion 53 Quasiconformal space 299 Quasielliptic space 285 Quasigroup 2 Quasihyperbolic space 285 Quasimatrix 53 Quasimetric space 290 296 Quasipseudo — Euclidean space 288 Quasipseudo — Riemannian manifold 307 Quasipseudoaltemion 53 Quasipseudoconformal space 299 Quasipseudoelliptic space 285 Quasipseudohyperbolic space 285 Quasisimple, algebra 37 Quasisimple, Lie group 289 Quasisymplectic, connection 326 Quasisymplectic, invariant of two lines 321 Quasisymplectic, space 321 Quasisymplectic, transformation 321 Quaternion 40 Quaternionic symplectic matrix 314 Quateroctonion 60 Quaterquaternion 48 Quotient, group 3 Quotient, space 6 r quasipseudo — Riemann ian manifold 307 r quasipseudoalternion 53 r quasisimple Lie algebra, group 289 r-quasi — Euclidean space 295 r-quasi — Riemannian manifold 307 r-quasialternion 53 r-quasiconformal space 299 r-quasielliptic space 291 r-quasihyperbolic space 294 r-quasimatrix 53 r-quasipseudo — Euclidean space 295 r-quasipseudoconformal space 299 r-quasipseudoelliptic space 291 r-quasipseudohyperbolic space 294 r-quasisimple algebra 38 r-quasisymplectic connection 326 r-quasisymplectic space 322—323 r-quasisymplectic trasformation 323 Radical 37 Radius of a hypersphere 10 188 Radius of curvature 2190 223 336 Radius-vector 7 Rank 62 Real elliptic, hyperbolic, pseudoelliptic, pseudohyperbolic spaces 219 Rectangular matrix 13 Rectilinear, apex of a hypercone 140 Rectilinear, generators 143 Reducible linear representation of a group 93 Reductive, Lie group 23 Reductive, space 26 Reflexivity axiom 6 8 Regular in Euclidean space 185 Regular in hyperbolic plane 265—267 Regular, conformal configuration 209 Regular, honeycomb in elliptic plane 265 Regular, polygon, polyhedron 184 Regular, projective configuration 156 Regular, Steiner triple system 214 Regular, topological space 5 Regular, vector 62 106 Reye configuration 156 Reye configuration, symbols 155 Riemann tensor 16 Riemann tensor in symmetric space 246—251 Riemannian manifuld 15 Riemannian manifuld of constant curvature 222 Riemannian manifuld, holomorphic curvature 248 Ring 2 Root, forms 63 Root, lattice 95 Root, vectors 63 76 80 Rotations 175 Rotor 14 Rumyantseva theorems 318 Satake diagram 81 scalar 3 Scalar, field 14 Scalar, product 8 SchefFers theorem 33 Schlafli theorem on regular polyhedra 184 Schrodinger equation 329 Screws in elliptic, hyperbolic space 281 Screws in Euclidean space 201 Screws in quasielliptic, quasihyperbolic etc, spaces 307 Sectional curvature 17 246 248—249 251 339 Segrean 112 151 Semicube 71 Semideterminant 43 45 Semigroup 2 Semioctonion 60
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