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| Sattinger D.H., Weaver O.L. — Lie groups and algebras with applications to physics, geometry, and mechanics |
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Название: Lie groups and algebras with applications to physics, geometry, and mechanics
Авторы: Sattinger D.H., Weaver O.L.
Язык: 
Рубрика: Математика/
Статус предметного указателя: Готов указатель с номерами страниц
ed2k:
Год издания: 1993
Количество страниц: 214
Добавлена в каталог: 26.02.2009
Операции: Положить на полку |
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| Предметный указатель |
action 69 72
Ad-nilpotent 125
Addition of angular momenta 176
Adjoint representation 28 39
Adjoint representation, action 96
Adjoint representation, eight-fold way 166
Ado’s theorem 37
Associativity 110 113
Automorphism 38 57 59 60
Baryons 164
Bifurcation 201
Bosons 50
Bosons, operators 50 51 175 186
Branching equations 202
Campbell — Baker — Hausdorff theorem 35
Canonical coordinate system 37
Carroll 182
Cartan criterion 29 119
Cartan decomposition 156
Cartan integers 137 138 171
Cartan matrix 143
Cartan structural equations 98 101—103 105
Cartan subalgebra 131 132 134
Casimir operator 179
Center 26
Christoffel symbols 100 106 108
Classical algebras 147—152
Clebsch — Gordon series 177
Coadjoint action 96 198
Connexion 99 106
Connexion, forms 100
Conservation laws 41 42 75
Creation and destruction operators 49 152 175 184
Curvature 100
Cyclic space 172
Derivation 38 59—61 122
Derivation, inner 122 129
Diagonalizeable 123
Diagonalizeable, simultaneously 123 166
Differential forms 63—67
Differential forms, invariant 75
Dirac 58 182
Direct sum 26
Dynkin diagram 143—146 170
Engel’s theorem 125
Enveloping algebra 172 179
Euclidean group 25 104
Euclidean group, invariance 71
Euler angles 37
Euler’s equations, incompressible fluid 75 105 107
Euler’s equations, rigid body 47 105
Exceptional algebras 31 146 147
Exterior derivative 65
Exterior derivative and connexions 97—100 102
Exterior derivative, frame invariance 70
Exterior product 63—67
Exterior product, frame invariance 70
Fermion operators 152 184 185
Flat connexion 102
Flow 58 61
Frame bundle 63 96 97 103—105
Frame invariance 70
Fundamental representations 170
Gell-Mann 164
Gell-Mann — Nishijima formula 164
Geodesies 105 106
Hamiltonian 41
Hamiltonian, harmonic oscillator 48
Hamiltonian, hierarchy 194 195
harmonic oscillator 48
Heat equation 25
Heisenberg group 4
Heisenberg group, algebra 25 43
Heisenberg group, isospin 52 163
Heisenberg group, uncertainty principle 124
Hilbert’s Fifth Problem 115
Homogeneous space 97 102
Hypercharge 164
Ideal 26 121
Infinitesimal generator 32 39 57 78
Invariant forms 90—96
Invariant function 80
Invariant measure 91—93
Invariant vector field 95 96
Ising model 186
Isometry group 97 98
Isomorphic 4 23
Isospin 41 52 163
Isospin-doublet 52
Isospin-triplet 168
Jacobi identity 22 112 115 192
Jordan decomposition 124
Kelvin’s theorem 75
Killing form 28 47 119 120 154
Korteweg — deVries equation 189
Kostant — Kirillov structure 197—199
Laplacian 71
Lax 189 190
Left invariance, associativity 113
Left invariance, Maurer — Cartan forms 111 113
Left invariance, measure 91—94
| Left invariance, metric tensor 106
Left invariance, vector fields, forms 90—94
Levi decomposition 27 119 122
Lie derivative 73
Line integral 62
Linear algebras 22
Linear groups 3
Local Group 36 81 110
Lyapounov — Schmidt 201
Manifold 109
Maurer — Cartan equations 94 95 99 103 109 113
Maurer — Cartan forms 111
Mesons 165 168
Metric tensor 9 28 97
Metric tensor on SO(3) 106
Minkowski space 16 97
Molien function 93 94 203—206
Navier — Stokes equations 57
Nilpotent algebra 27 121
Nucleon 52 163
Observables 123
Omega-minus particle 169
One form 62
One form, left invariant 90 93 94
Onsager 186
Over-determined system 113 114
Pauli spin matrices 13 15
Pion 168
Poincare group 72
Poincare half plane 9 97 99
Poisson brackets 41
Poisson brackets, Gardner — 191
Prolongation 77—79
Quarks 165 166—170 177
Quarks, anti-quarks 166—170 177
Quotient algebra 26
Radical 27 122
Real basis 153
Real compact real forms 154—156
Real forms 24 153
Regular element 134
Representation 4
Representation, fundamental 170 174
Representation, irreducible 170 172 173
Representation, Lie algebra 24
Representation, spinor representations 5 9
Riemannian connexion 97 99 106
Riemannian manifold 97
Rigid motions 104
Roots 131 132
Roots, diagram 140
Roots, figure 132
Roots, fundamental, or simple 142
Roots, spaces 132
Roots, string 137
Roots, vectors 131 132
Schur’s lemma 180
Semi-direct sum 26
Semi-simple algebra 27 119
Simple algebra 27
Sine — Gordon equation 189
Solvable algebra 27 119
Spinors 9
Spinors, representations 5 178 185
Stokes’ Theorem 66
Strangeness 41 164
Structural equations 98 101
Structure constants 22 28 95
Subalgebra 26
Symmetries, conservation laws 85—87
Symmetries, differential equations 80—84
Symplectic transformation 44
Tangent space 61
Tensor product 166 175—177
Three-wave interaction 196
Torsion 100
Transport theorem 74
Triangulable 125
Triangulable, Lie’s theorem 125
Unimodular 92
Universal covering group 5
Universal covering group, Lorentz group 17 18
Universal covering group, Moebius group 8
Universal covering group, SO(3) 10—14
Vector analysis 71
Vector field 58 61
Vector invariant 75 95 96
Wedge product 63
Wedge product of representations 177
Weight 151 167 170
Weight, diagram 167
Weight, dominant 171
Weight, fundamental 174
Weight, highest 172 180
Weight, spaces 171
Weight, vector 170
Weyl basis 30
Weyl group 141 150 151 171
Weyl reflection 140 141
Weyl theorem 154
Weyl — Chevalley normal form 133
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