Naimark M.A., Stern A.I. — Theory of Group Representations :: Электронная библиотека попечительского совета мехмата МГУ

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Naimark M.A., Stern A.I. — Theory of Group Representations

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Название: Theory of Group Representations

Авторы: Naimark M.A., Stern A.I.

Аннотация:

This book is written for advanced students, for predoctoral graduate students, and for professional scientists—mathematicians, physicists, and chemists who desire to study the foundations of the theory of finite-dimensional representations of groups.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 567

Добавлена в каталог: 31.10.2010

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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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