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| Авторизация |
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| Boerner H. — Representations of Groups |
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| Предметный указатель |
Abelian group 26
Additive group of angles 175
Additive group of angles, complex numbers 175
Additive group of angles, real numbers 173
Adjoint representation 91
Adjoint representation of the rotation group 234
Algebra 8
Algebra, Clifford 267
Algebra, de Broglie 299
Algebra, Dirac 298
Algebra, Kemmer 299
Algebra, semi-simple 72
Alternating elementary sum 241
Alternating group 29
Alternating group, characters 206
Alternating group, representations 197
Alternating polynomial 241
Alternating representation 80 95 102 103
Antihermitian 12
Antisymmetric (matrix) 12
Antisymmetric (tensor) 128 148
ASSOCIATED 96
Automorphism 27
Automorphism, inner 27
Basis 2
Basis change 6
Basis, adapted 3
Bauer, F.L. 316
Birkhoff, G.I. 316
Bisymmetric transformation 133
Bivins, R.L. 216
Block rules 5
Boerner, H. 299 316 317
Boundary of a frame 194
Branching theorem (full linear group) 160
Branching theorem (rotation group) 251 253
Brauer, R., VIII 275 316
Burnside's theorem 69 192
Burnside, W., VII. 69 316
Canonical coordinates 40
Canonical parameter 38
Cartan, E. VIII 33 34 167 232 234 249 267 301 305 316
Centre 70 82 86
Centre lattice 227 228 231
CHARACTER 76
Character, composite 76
Character, generalized 211
Character, simple 76
Character, table 76
Characteristic 184
Characteristic of rational integral representation of full linear group 185
Characteristic polynomial 12
Characters of a direct product 83
Characters of continuous groups 92
Characters of the alternating group 206
Characters of the regular representation 80
Characters of the rotation group 247
Characters of the symmetric group 192
Chevalley, C. 41 90 317
Class function 76
Class of conjugate group elements 27
Class of conjugate group elements (alternating group) 31
Class of conjugate group elements (symmetric group) 31
Class of equivalent representations 50
Class sum 72 82 86
Clebsch — Gordan formula 290
Clifford algebra 267
Clifford numbers 267
Clifford, A.H. 100 317
Clifford, W.K. 265 317
Commutativity of matrix systems 22
Complete reducibility, theorem of 49
Completely reducible 21
Complex orthogonal group 34
Complex orthogonal group, fundamental representations 264
Complex orthogonal group, spin representations 282
Composite character 76
Conjugate (group elements) 27
Conjugate (representations) 96
Continuous groups 32
Convex lattice point figure 294
Coordinate transformation 6
Coset 27
Covering group 219
Covering space 222
Cycle notation 28
De Broglie algebra 299
de Broglie, L. 316
Decompose 17 21 48
Degree of a representation 47
Diagonal form 13
Dimensions of a linear subspace 3
Dimensions of a matrix group 32
Dimensions of a vector space 1
Dirac algebra 298
Dirac, P.A.M. 265 267 317
Direct product 83
Direct sum 3
Direct sum of full matrix rings 17
Effective space 45
Eigenvalue 12
Eigenvector 12
Einstein, A. 127 303
Elementary sum, alternating 241
Elementary sum, invariant 240
Equivalence mapping 20
Equivalence mapping of left ideals 60
Equivalence of left ideals 56
Equivalence of representations 48
Equivalent 20
Even permutation 29
Exponential function, matrix 34
Factor group 27
Faithful 47
Four-group 32
Frame 104
Freudenthal, H. 283 317
Frobenius, G. VI 69 86 104 190 192 208 317
Full linear group 32 315
Full linear group, characteristics 184
Full linear group, representations 126 171 172 182
Full Lorentz group 300 303
Full Lorentz group, fundamental representations 306
Fundamental domain 228
Fundamental representations of Lorentz group 306
Fundamental representations of rotation group 256
Gamba, A. 184 198 199 317
Garnir, H.G. 114 184 317
Gelfand, I.M. 300 317
Generating idempotent 58
Generating idempotent in tensor space 141 154
Generating unit 58
Gordan, P. 289
Group 26
Group, algebra 53
Group, embryo 42
Group, numbers 54
Group, ring 53
Haar, A. 317
Hamermesh, M. 316 317
Heine, V. 316 317
Hermitian adjoint matrix 10
Hermitian form 11
Hermitian matrix 11
Hoenl, H. 299 317
Homomorphism 27
Homomorphism theorem 27
Homotopic 217
Homotopy class 217
Hook 196
| Horizontal permutation 104
Hurwicz, A. 317
Hypercomplex system 8
Ideal 55
Idempotent 7 58
Identity representation 80 102 103
Index of a subgroup 27
Inertia, rule of 15
Infinitesimal ring 36
Infinitesimal ring of adjoint representation 91
Infinitesimal ring of rotation group 268 290 315
Infinitesimal ring, representation of 90
Inner automorphism 27
Integral over a class function 236
Integration 42
Invariant elementary sum 240
Invariant polynomial 240
Invariant subspace 12 20
Inverted representation 62
Irreducible (matrix system) 20
Irreducible (representation) 47
Isomorphism (group) 27
Isomorphism (ring) 56
Isomorphism (vector space) 3
Jacobi's identity 38
Jordan normal form 14
Jordan, P. 317
Kemmer algebra 299
Kemmer, N. 296 299 317
Kernel of a homomorphism 27
Klein's four-group 32
Kondo, K. 317
Krafft, G. 309 313 318
Kronecker power 132
Kronecker product 18
Kronecker product (representations) 126
Kronecker product of representations of full linear group 201
Kronecker product of representations of full symmetric group 202
Kronecker product, augmented 203
Kronecker square 127
Kronecker symbol 5
Lattice in Stiefel diagram 227
Ledermann 26 318
Left ideal 55
Left translation 43
Lie group 41
Lie ring 41
Lie, S. 92
Linear hull 53
Linear mapping 3
Linear subspace 3
Linear transformation 3
Linear, group 32
Linearly independent (subspace) 3
Linearly independent (vectors) 3
Linearly independent components (tensor) 150
Littlewood, D.E. VII 184 318
Lomont, J.S. 316 318
Lorentz group 300
Lorentz group, fundamental representations 306
Lorentz group, ordinary 301 312
Lorentz group, ordinary proper 309
Lorentz group, proper 302 305 308
Lorentz matrix 300
Lorentz matrix, improper 303
Lorentz matrix, proper 302
Maak, W.V. VIII 37 90 318
MacLane, S. 1 318
Mapping, linear 3
Maschke's Theorem 48 75
Maschke, H. 318
Matrix 4
Matrix algebra 9
Matrix exponential function 34
Matrix groups 32 36
Matrix product 5 6
Matrix ring, full 8
Metropolis, N 318
Minimal ideal 55
Murnaghan — Nakayama rule 196
Murnaghan, F.D. VII 166 184 198 206 290 316 318
Nakayama, T. 184 318
Natural representation 114
Neumark, M.A. 300 318
Newell, M.J. 318
Noether, E. VII VIII 318
Non-decomposing representations 172
Non-singular (matrix) 5
Normal (representation) 74
Normal form, Jordan 14
Normal subgroup 27
Odd permutation 29
Order (class of conjugate elements) 28 30
Order (group) 26
Order (permutation cycles) 29
Ordinary Lorentz group 301 312
Ordinary proper Lorentz group 309
Ordinary rotation group 287
Orthogonal (matrix) 12
Orthogonal group 33 261 315
Orthogonality relations (characters) 78 94
Path 215
Pauli matrices 270 287
Peirce decomposition 59
Permutation 28
Perron, O.M. 318
Peter, F. IX 95 246 318
Pontrjagin, L. 41 42 90 318
Primitive idempotent 60
Principal fundamental domain 229
Principal term of an elementary sum 240
Principal weight 234
Projection 7
Prokop, W. 86 319
Proper Lorentz group 302 305 308
Proper Lorentz matrix 302
Proper orthogonal group see "Rotation group"
Proper orthogonal matrix 12
Quadratic form 10
Rank of a matrix 5
Rational integral representations 132
Real linear group 33 315
Real linear group, representations 164 172 182
Real orthogonal group see "Orthogonal group"
Real unimodular group 33 315
Real unimodular group, representations 164 172 176
Reducible 20 47
Regular boundary piece 195
Regular element (toroid) 222 225 230
Regular representation 55 69
Reisch, P. 319
Representation 46
Representation degree 47
Representation of direct product 83
Representation of group ring 54
Representation of infinitesimal ring 90
Representation space 46
Representation, adjoint 91
Representation, natural 114
Representation, regular 55 69
Reversible 5
Richardson, A.R. 184 319
Right ideal 55
Right invariant 236
Right multiplication 56 64
Right translation 43
Ring 8
Ring tensor 145
Robinson, G. de B. 319
Roots of rotation group 234
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