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| Gilmore R. — Lie Groups, Lie Algebras and Some of Their Applications |
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| Предметный указатель |
Schroedinger hamiltonian 429 430
Schroedinger, E. 427 435
Schur’s lemma 110 118 200 232
Schwartz inequality 311
Second criterion of solvability 216 253—255
Second order 95
Secret tool 73
Sectional curvature 487
Secular equation 124 216 218 237—248 249 251 263 270 273 280 319 354 355 357 362 422
Secular polynomial 243
Segal, I.E. 506
Self-conjugate subgroup 72
Semicanonical parameterization, of a group 402—406
Semidirect product 492
Semidirect product group 83 158
Semidirect sum 225 256 261
Semisimple 233 234 236 240 251 256—261 262—273
Semisimple algebra 278 280 293 301 306 308 316 317 320 321 323 324 331 332 334 336 344 436 449 452 463 477 478 483
Semisimple group 83 114 321 333 334 346
Semisimple Lie group 158
Semisimple root space 283 284 289 422
Separability 59
Separation of variables 102
Separation of variables in a Lie algebra 486 487
Separation of variables, group theoretic version 396
Sesquilinear 38
Sesquilinear antisymmetric metric 187 195
Set 1 10 14 19 20 57
Several complex variables 372
Shah, K.T. 506
Sheet 71 74 75 84
shift operators 149
Shirkov, D.V. 56
Sibling algebras 286
Signature 377 434
Similarity transformation 263 341 343 344
SIMPLE 236 238 240 251 252 257 261
Simple algebra 278—280 308 310 316 320 324 328 337 339 348 436 449 463 478 492
Simple contractions 436—463
Simple group 83 321 327 334
Simple invariant subalgebra 280
Simple Lie algebra 422
Simple Lie group 158
Simple matrix group 493
Simple negative root 297 300 302
Simple positive root 297 300 302—306
Simple root space 278 298 300 301 308 346
Simple roots 278 299 298—307 315 316
Simply connected 71 85 87 108 110—112 122 129 131 134—136 427
Simultaneous linear partial differential equations 100
Sine 15
Singer, I.M. 56 86
Single complex variable 431
Single-sheeted hyperboloid 407
Singly connected 131
singular 237
Singular matrix 375
Singular metric 255
Singular transformation 436 446 448 449 459 463 464 493
Skew line on a torus 179 329 330
Skew-symmetric 333 338
Skew-symmetric metric 47 48 51 183 185
Sl(1, q) 52 121 122 124 126—129 131 134 143 144 178
SL(2, C) 52
Sl(2, q) 52
Sl(2, r) 52 119 389
Sl(3, r) 273
Sl(4, r) 52 85 350
SL(n) 481
Sl(n, c) 184—186 189 190 192 198—199 339 412 413
Sl(n, q) 47 48 50 51
SL(n, R) 2 37 47 50 184 186 190 197 213 339 347 352 356 359 365 412 414 415
Slice 156
SO(1, 1) 203 211
SO(2) 199 203—210 212 334 346 378—380 445 478
SO(2, 1) 52 202—205 209 211 212 379—380 407 431 445 478 479
SO(2, 2) 52
SO(2n) 118 218 501
SO(2n), volume of 399
SO(2n+1), volume of 399
SO(2n+1, c) 294
SO(2n, c) 294
SO(3) 52 84 85 111 118 120 124 126—132 134 143 144 147—149 152 178 179 203 207—209 212 334 367 378 379 381 395 407 444 445 478 479 494 502
SO(3), commutation relations of 209
SO(3, 1) 52 214 395 401 428 502
SO(3, 2) 52 457
SO(3, 3) 52 332 349 350
SO(4) 52 214 428
SO(4, 1) 52 457
SO(4, 2) 52 332 349 350 397 398 460
SO(5) 52
SO(5, 1) 52 332 349 350
SO(5, 2) 397 398
SO(6) 52 332 349 350
SO(n + 1, n; r) 294
SO(n, 1) 451—455 480
SO(n, 2) 374—378
SO(n, c) 186 187 189 191 192
SO(n, n; r) 294
SO(n, r) 110 118 186 187 191 192 197—200 214 274 330 331 334 347 352 356 358 359 365 368 382—388 398—400 404 405 412—414 425 450 452—455 457 459 479 480
SO(p, q) 187 191 197 199 200 331 342 347 348 356 358 382 383 403—404 412—414 452 453 481 491
SO*(2n) 47 48 51 187 191 192 195 199 343 344 348 356 358 359 413 414 427
SO*(4) 52
SO*(6) 52 349 350
Solvability, first criterion of 216 243—244 273
Solvability, second criterion of 216 253—254 273
solvable 224 227—230 232—234 238 241 243—246 250 253—258 263 273 274 304 469
Solvable algebra 224 225 278 279 317
Solvable invariant subalgebra 234 236 243 425 427
Solvable Lie group 158
Soni, R.P. 23
South pole 133 169 389
Sp(2, r) 52
Sp(2n, c) 45—52 188 189 191 294 343 415
Sp(2n, r) 45—52 188 191 197—199 294 344 356 358 359 412 415 426 427 501
Sp(4, r) 52
Sp(n, q) 45—52
Space, linear vector 5
Space-time 41 214
Space-time event 22
span 230 279
Special functions 15 100 326
Special linear groups 24 37 53
Special metric-preserving groups 47
Special relativity 38 43
Speiser, D. 181 435
Sphere 169 170 202 203 206—209 365 378 379 407 444 445
Sphere surface 85
Sphere,  133
Sphere,  131
Sphere,  131
Spherical coordinates 170 393
Spherical harmonics, contraction to Bessel functions 495
Spherical harmonics, contraction to harmonic oscillator eigenfunctions 496
Spherical harmonics, generating function for 181
Spherically symmetric potential 427
Spin 53 146—149 162—168 170 171 176 177
Spin (3) 111 427
Spin (4) 427
Spin (5) 427
Spin (6) 427
Spin (n) 111 334 427
Spin matrices 17
Spin, angular momentum 23
Spin, down 146 147 148 158
Spin, echo 176 177 178
Spin, precession 166 176 177 178
Spin, up 146 147 148 158
Spin-orbit coupling 276
Spin-statistics relationship 121 146
| Spinor 28 147
Spivak, M. 86
square-integrable 21
Stability group 367 368 383 387
Standard topology,  59
Standard topology,  60
Statistical physics 496
Statistical theory of energy levels 214
Statistics, Bose — Einstein 146
Statistics, Fermi — Dirac 146
Stegun, I.A. 435
Sternberg, S. 86
Straight line 111 119 127 328 329
Straight line in Lie algebra 111—113
Strangeness 121 146
Stress-energy-momentum tensor 146
Structure constants 95 100 102—106 216 217 219 222 223 248 249 251 259 261 266 267 270 273 322 334 336 338 436 443 446 448 449 475—477 486—488
Structure constants as matrix elements 105—106
Structure constants for associative algebra 12
Structure constants for semisimple algebra 279
Structure constants, symmetries of 266 268 280
Structure function, of Lie group 87
SU(1, 1) 52 201—205 209 478
SU(2) 52 111 118 120—154 158 160 178 179 202 203 207—209 253 334 478
SU(2, 1) 273
SU(2, 2) 52 350
SU(3) 180 214 272 273
SU(3, 1) 52 350
SU(4) 52 350
SU(N) 48 50 110 118 179 190 192 196—200 214 239 274 278 339 340 347 412 413 425 427
SU(p, q; c) 200 340 347 348 412 413 482 491
SU*(2n) 47 48 51 183 185 186 190 192 196 199 213 341 347 348 352 356 359 366 412 413 415
SU*(4) 52 350
Subalgebra of Lie algebra 220—229
Subalgebra, Cartan 246 247
Subfield restriction 197—198 199
Subgroup 2
Subgroup, abelian 94
Subgroup, conjugate 94
Subgroup, discrete 87
Subgroup, invariant 87 94
Subgroup, one-parameter 94
Subset 2 57
Subsidiary conditions, for roots 280
subspace 9
Subspace, orthogonal complementary 200
Sum, semidirect 225
Supermultiplet, Wigner model 349
Surjective 18
symmetric 8
Symmetric matrix 9 13 338 344 350 351 356 365
Symmetric matrix representation, of group 30—33
Symmetric metric 40
Symmetric nondiagonal metric 43
Symmetric reduction, in tensor space 30—33 53
Symmetric space 431
Symmetric spaces, real forms of 406—422
Symmetric spaces, real forms of, table of 412—419
Symmetric subspace 53
Symmetric tensor 30—32
Symmetrization 9
Symmetrized bases 30—33
Symmetrized operator product 149
Symmetrized order 172 173
Symmetrized subspaces 30—33
Symmetry vi
Symmetry for generators of classical groups 189
Symmetry group vi 349
Symplectic algebra 188 191
Symplectic ensemble 214
Symplectic groups 45 182 187—189 191 200 295—297
Symplectic groups, expansion of 482—483
Symplectic symmetry 188 189 343 344 345 347
t (matrix transpose) 22 266
Talman, J.D. x 23 119
Tangent plane 386
Tangent vector 35
Taylor series 126
Taylor series expansion 77
Taylor’s Theorem 87 90 111—118
Tchebicheff polynomials 54
Tensor 28 217
Tensor product 28
Tensor product representations 136
tetrahedron 20 313
Thermal average 496—498
Thermal equilibrium 176
Third order iterations 116
Thomas commutation relations 502—504
Thomas decomposition 502—504
Thomas precession 214 502—504
Thomas, factor  504
Thomas, H. 181 506
Thorpe, J.A. 56 86
Tickling field 162 165 166
Topological group 57 63 75 84
Topological properties 199—212
Topological properties of Lie group 326—334
Topological space 58 65 78 91
Topological space, underlying 85
Topological structure, on continuous group 63
topology 58 353
Topology, cube 59 60
Topology, sphere 59 60
Torsion 132
Torus,  or  71 72 131 179 329 330
Trace 175 183—186 248—252 263 265 269 275 276 339—341 357 365 422 497
Trajectory 168
Transcendental function 364
Transformation groups 100
Transformation, Lie group of 87—91
Transition operator algebra 349
Transition probability 162 167
Transitive 366
Translation, left 92
Translation, right 92
TRANSPOSE 22 266
Transpose of a matrix about major diagonal 41 42
Transpose of a matrix about minor diagonal 42
Triangular matrices, lower 139 157 158 302
Triangular matrices, upper 139 157 158 302 304
Triangular patterns 402—406
Trigonometric identities 15
Tsetlein, M.L. 277 435
U(1) 52 145 146 201 203—209
U(1, q) 52 120 122 123 124 143 144
U(2) 120 121 136 142—145 159 178 214 460 463 495
U(2, 2) 460
U(3) 180 424
U(n) 45—52 184 185 190 192 195 196 197—199 214 239 274 343 344 347 356 358 359 393 394 389—400 414 415 427
U(n), volume of 399
U(n; q) 45—52 196
U(p, q) 45—52 185 190 197 358 405 413—415 421
U(p, q; Q) 45—52 197—199
Unbounded domain 370—372 377 378
Unfaithful 14 105 239
Unimodular classical group 110
Unimodular groups 183
Unimodular matrix 366
union 58 59
Unit circle 21
Unit disc 378—380 382
Unit matrix 9
Unit vector 307
Unitary algebra 185 190
Unitary ensemble 214
Unitary group 2 45 122 182 183—186 190
Unitary groups, expansion of 481—482
Unitary irreducible representations 55 140 141 143 145 153 179 349
Unitary irreducible representations for SU(2) 153
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