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Boerner H. — Representations of Groups
Boerner H. — Representations of Groups



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Название: Representations of Groups

Автор: Boerner H.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1963

Количество страниц: 336

Добавлена в каталог: 11.11.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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