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| Авторизация |
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| Naimark M.A., Stern A.I. — Theory of Group Representations |
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| Предметный указатель |
AD 357
Additive character of a field 122
Adjoini representation (of a Lie algebra) 341
Adjoini representation (of a Lie group) 357
Adjoint 31
Adjoint group 362
Ado's Theorem 496
Aleksandrov, P.S. 165
Algebra 80
Algebra of functions 175
Algebraic cornmutatoi 238
Algebraically nilpotem 239
Algebraically nilpotem, solvable 239
Alternating group 17
Analytic 266 269
Analytic coordinates 324
Analytic coordinates, function 324
Analytic coordinates, isomorphism 327
Analytic coordinates, manifold 324
Analytic coordinates, representation 348
Analytic coordinates, space 275
Analytical homomorphism 346
Antihomomorphism 10
Antisymmetric (tensor) 280
Automorphism group 15
Basis (representation) 279
Bernoulli numbers 498
Bicompact 165
Borel subgroup 552
Burnside’s Theorem 68
Campbell Hausdorff formula 502
Campbell Hausdorff formula, series 502
Canonical homomorphism (natural mapping) 10
Canonical homomorphism (natural mapping), isomorphism 355 370
Canonical homomorphism (natural mapping), model 20
Canonical homomorphism (natural mapping), model (of the irreducible finite dimensional representation) 553
Canonical homomorphism (natural mapping), neighborhood 354
Canonical homomorphism (natural mapping), realization 260 295
Canonical homomorphism (natural mapping), system (of coordinates) 354
Cartan’s criterion 389
Cartan’s criterion, factorization 452
Cartan’s criterion, numbers 420
Cartan’s criterion, subalgebra 407
Cartan’s criterion, theorem 507
Casimir element 397
Center of I 340
Centered (system of sets) 165
CHARACTER 52 56 194 459
Character (of an induced representation) 114
Characteristic of a field 118
Circic (in a field) 118
Classical (Lie algebra) 449
Classical (Lie algebra), solution 552
Closed direct sum 227
Commutative (algebra) 84
Commutative (algebra), abelian group 1
Commutative (algebra), abelian Lie algebra 339
Commutator (or a group) 238
Commutator (or a group) of vector fields 334
Compact (topological group) 165
Compact (topological group), Lie algebra 4
Compact (topological space) 165
Complejsilication ol the representation 372
Complete set (of able representations) 67
Completely reducible (representation) 35
COMPLEX 84
Complex (n-dimensional vectoi group) 22
Complex (n-dimensional vectoi group), symplectir group 283
Complex (n-dimensional vectoi group), unimodular orthogonal group 283
Complex analytic 550
Complex hull (of the real Lie algebra) 371
Complex-antianalytic 550
Component 302
Conjugacy class 15
Conjugate (homomorphism) 370
Conjugate-representation 199
Connected component 231
Connected component, topological group 233
Connected component, topological space 129
continuous curve 137
Continuous curve, homomorphism 145
Continuous curve, isomorphism 145
Convolution (of functions) 90 212
Coordinate neighborhood 32
Coset 4
Covering space 302
Cramer factorization 238
CYCLE 17
Cycle group 4
Cycle, length of 17
Decomposition (of the regular representation) 193
Der(A) 368
Derived ideal 373
Descending central series 373
Differentiation (in an algebra) 368
Differentia] (of a mapping) 329
Dimension (of a manifold) 324
Dimension degree (of the representation) 24
Direct product (of groups) 71
Disconnected (topological group) 233
Disconnected (topological group), topological space 229
Discrete (topology) 132
Dominant Weyl chamber 450
Dynkin diagram 4
Eigenfunction 190
Eigenvalue 190
Elements of the cycle 17
Engel’s theorem 374
Euclidean space 46
Euler’s angles 180
Exponential mapping 352
Facto. algebra (of a Lie algebra) 339
Factor group 6
Field 118
Field of residues 118
finite 2
Finite field 118
Fourier coefficient 70
Freudenthal's formula 473
Frobenius' duality theorem 113
Fundamental Weyl domains 450
Gaussian sum 125
Gauss’s decomposition 46 250 287 527 530 533
Gel'fand, I.M. 153
Generating function 553
Gram's decompositions 254
Group 1
Group algebra (of symmetrzer group) 13 88 213
Group algebra of dilations of the line 16
Group algebra of fractional-linear transformations 16
Group algebra of linear transformations of the line 16
Group algebra of residues 7
Group algebra of rotations of the circle 16
Group algebra of translations of the line 16
Group, abelian 1
Group, commutator 1
Group, cyclic 4
Group, finite 2
Group, infinite 2
Haai measure 539
HausJorff space 137
Height (rank) of a solvable (nilpotent) Lie algebra 373
Hermitian (form) 45 84
Highest vector (of a representation) 454
Highest weight (of a representation) 295 454
Homogeneous 399
Homogeneous, chain 430
Homogeneous, space 13
Homogeneous, tensor 392
Homomorphism 9 82 137 338
| Homomorphism, canonical 10
Horn (T,S) (or Horn G(T,S)) 55
Ideal 81
Ideal of inner differentiations 369
Identity representation 25
Image 8
Image of the vector field 334
Imprimitivity theorem 117
INDEX 4
Induced representations 112
Inductive (character) 295
Infinite 2
Intertwining number 55
Intertwining number, operator 55
Invariant form 388
Invariant form, mean 60 61 183
Invariant form, subgroups 15
Inverse image 8
Involution 84
Irreducible 24 35 162
Irregular (coset) 271
Isomorphism 10 82 338
Iwasawa’s decomposition 533 549
Jacobi’s identity 334 337
Jordan canonical form 51
Jordan Holder series 373
Killing form 389
Kostant's formula 473
Left invariant differential operators 399
Length (of a cycle) 17
Levi — Malcev Theorem 495
Lexicographic ordering 418
Lie algebra 337
Lie algebra, group 341
Lie algebra, subalgebra 338
Lie's theorem 243 377
Lie's theorem, third theorem 51
Linear group 142
Local homomorphism 309
Local homomorphism, isomorphism 310
Locally compact 168
Locally compact, connected 302
Locally compact, convex 161
Locally compact, simply connected 312
Mapping 8
Method of Zinvariants 274
Minimal algebra 81
Multiple of the irreducible representation 203
Multiplicative character (of a field) 121
Mutually conjugate (representation) 86
n-dimensional torus 23
Natural topology 132
Natural topology, topology of the group 140
Nilpotent 241
Nilpotent, radical 383
Nilradical 383
Nondegenerate (involution) 84
Nonsingula 217
Normal divisor 5
Normal divisor, space 159
Normal divisor, topological space 170
One-to-one 8
Open submanifold 326
Operator (of a representation) 85 162
Orbit 13
Ordered vector space 418
Orthogonal complement 29 400
Orthogonality relations 67 72 189
Orthonormal 47
Permutation 12
Plancherel's formula 71 193
Poincare — Birkhoft in theorem 394
Polyvectors 280
Positive root 419
Pre — Hilbert space 46
Product (of manifolds) 327
Projection 48
Projection (of a manifold) 327
Projection of a point 138
Quadratic extension 127
Quadratic residue 124
Quotient algebra 82
Radical 383
Real complex Lie algebra 337
Real complex Lie group 341
Real or complex analytic representation 348
Reducible (representation) 24
Region 229
Regular 330
Regular (coset) 271
Regular (coset), element 407
Regular (coset), representation 14
Replica of an element 385
Representation 23 150 161
Representation (of an algebra) 85
Representation (of an algebra), operator 23
Representation (of an algebra), spacc 23
Restriction 9
Root (of a Lie algebra) 406
Schur's lemma 26 55
Self-representation 24
Semi norm 160
Semi simple 241
Semi simple, lie algebra 383
Semidirect produce (of Lie algebra) 514
Semidirect produce, product of Lie groups 512
Semidirect produce, sum (or linkage) 37
Separated (space) 137
Signature 269
Signature (of the character) 296
Simple (algebra) 81
Simple (algebra), Lie algebra 383
Simple (algebra), root 419
Simple (algebra), topological group 241
Simply connected (space) 305
solvable 241
Solvable, group 239
Space of representation 85 162
Spinor group 301 323
Stationary group 19
Stone's theorem 171
Structural constant of the Lie algebra 338
Strung topology 159
Subalgebra 81
Subgroup 3
Submanifold invariant 15 335
Sufficient (set) 160
Support 167
symmetric 84
Symmetric group 13
Symmetric group, group 98
Symmetric group, subset 160
Symmetric group, tensor 280
Tangent space (to a manifold) 327 336
Tensor algebra 392
Tensor algebra, pioduct (of representations) 370
Tensor algebra, product 41
Tensor algebra, representation (of a group) 158
Terminal point 137
Theorem (H. Weyl) 402
Theorem (H. Weyl) of Weiertras 174
Topological automorphism 145
Topological automorphism, group 139
Topological automorphism, isomorphism 145
Topological automorphism, linear space 158
Topological automorphism, properties 137
Topological automorphism, space 132
Topologically equivalent (spaces) 149
Trace 50
Trajectory 13
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