Kirillov A.A. — Elements of the Theory of Representations :: Электронная библиотека попечительского совета мехмата МГУ

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Kirillov A.A. — Elements of the Theory of Representations

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Название: Elements of the Theory of Representations

Автор: Kirillov A.A.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1976

Количество страниц: 256

Добавлена в каталог: 11.04.2008

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

Предметный указатель

$T_{0}$ -space      7
Abelian group      12
Absolutely continuous measure      40
Absolutely simple Lie algebra      92
Abstract group      12
Action (of a group) on the left      13
Action (of a group) on the right      14
Adjoining a unit      25
Adjoint representation of a Lie algebra      97
Adjoint representation of a Lie group      97
Admissible chart      63
Admissible subalgebra      236
Ado’s theorem      88
Aleksandrov’s line      63
Algebra of type I      60
Algebra over K      32
Algebraic integer      157
Algebraic manifold      68
Algebraic number field      28
Algebraically irreducible representation      110
Almost everywhere      39
Alternating group      262
Amenable group      129
Analytic vector      155
Antirepresentation      14
Associativity      12
Atlas      62
Automorphism      11 13
Banach algebra      45
Banach space      37
Banach — Steinhaus theorem      42
Base      78
Base for a topology      6
Basis      31
Basis measure      54
Bicommutant      58
Bifunctor      6
Bigebra      178
Binary relation      2
Borel set      6
Borel — Weil — Bott theorem      140
Boundary of a manifold      77
Bounded set      41
Burnside’s Theorem      140
C*-algebra      49
C*-algebra of a group      143
Campbell — Hausdorff — Dynkin formula      108
Canonical embedding      4
Canonical mapping      2
Canonical matrix      92
Canonical parameter      85
Canonical projection      4
Cartan’s criterion      92
Cartan’s subalgebra      93
Category      3
Central extension      20
centralizer      17
Change of scalars      111
Character group      167
Character of a finite dimensional representation      156
Character of a infinite dimensional representation      161
Character of Banach algebra      46
Chart      62
Choquet’s theorem      42
Class $C^{k}$       63
Classical simple algebra      92
Clifford algebra      34
Closed form      76
Closed operator      114
Closed set      6
Co-adjoint representation      226
Coboundary      10 21
Coboundary operator      10
Cochain      10
Cocycle      10 21
Cohomology group      21
Coinduced representation      187
Commutant      58
Commutation      86
Commutative algebra      87
Commutative group      12
Commutator of vector fields      72
Compact      7
Compact operator      42
Complete measure      39
Completely continuous operator      42
Completely irreducible representation      112
Completely reducible representation      110
Completion      9
Complex manifold      68
Complexification      111
Component of a section      79
Conjugate representation      109
Conjugate subgroup      15
Connected set      7
Continuous product of algebras      60
Continuous sum of spaces      58
Continuously diagonal operator      58
Contragredient representation      109
Contravariant functor      5
Contravariant tensor      33
Convolution      140
Convolution of generalized functions      148
Cotangent bundle      79
Countably additive measure      38
Countably normable space      37
Courant’s priniciple      56
Covariant functor      5
Covariant tensor      33
Cross norm      42
Cross section      79
Cyclic group      16
Cyclic representation      53
Cyclic vector      53
De Rham cohomology ring      76
Decomposable extension      20
Decomposable operator      58
Decomposable representation      110
Decreasing filtration      26
Derivative along a vector      69
Derivative of a family of mappings      71
Derivative of a mapping      70
Derivative of a measure      40
Determining (family of prenorms)      36
Diagonal operator      58
Diffeomorphic manifolds      64
Diffeomorphism      64
Differentiability along a vector field      73
Differential      74
Differential form      74
Differential form of type (0,r)      82
Differential of a function      70
Dimension of a minifold      62
Dimension of a vector space      31
Direct sum      31
Direct sum of bundles      79
Directed set      3
Direction      3
Disjoint measures      40
Disjoint representations      109
Distance      8
Division algebra      27
Dixmier — Glimm — Sakai theorem      162
Dolbeault’s theorem, generalized      82
Double coset      16
Dual category      4
Dual group      167
Dual module      30
Dual object of a group      113
Dynkin diagramm      94

Engel’s theorem      91
Envelopping algebra      149
Epimorphism      13
Equivalent atlases      67
Equivalent extensions      19
Equivalent measures      40
Equivalent representations      48 109
Even permutation      262
Exact form      74
Exponential Lie group      103
Exponential mapping      103
Extension (of a group)      18
Exterior algebra      34
Exterior differentiation      74
Exterior product      34
Factor      62
Factor group      15
Factor Lie algebra      33
Factor module      29
Factor representation      110
Factor ring      25
Factor set      2
Factor space      7
Faithful representation      13 48
Fiber      78
Field      27
Filtering to the right      3
Filtration      26
Finite measure      39
Finite representation      115
Flag manifold      291
Formal dimension      139
Fourier transform      166
Free algebra      33
Free K-module      29
functor      6
Fundamental direction      9
Fundamental group      9
G-orbit      14
Garding space      153
Gel’fand theorem      49
Gel’fand transform      46
Gel’fand — Kirillov conjecture      152
Gel’fand — Mazur theorem      45
Gel’fand — Naimark theorem      83
Gel’fand — Raikov theorem      146
Generalized infinitesimal character      165
Generalized infinitesimal generating function      232
Generalized infinitesimal Gleason — Montgomery — Zippin theorem      83
Graded      26
Graph of an operator      121
Grassmann algebra      34
Grassmann manifold      65
Grothendieck group      110
Group      12
Group algebra      140
Group ring      139
Hahn — Banach theorem      42
Hamiltonian vector field      231
Hausdorff space      7
Heisenberg group      237 287
Hermitian element      48
Hilbert space      37
Hilbert tensor product      44
Hilbert — Schmidt operator      44
Holomorphic bundle      80
Holomorphic cross section      80
Holomorphicaly induced representation      204
Homogeneous algebra      60
Homogeneous G-space      15
Homogeneous symplectic manifold      233
Homomorphism      12
Homotopic mappings      9
Homotopy class      9
I-adic topology      27
Ideal of a Lie algebra      89
Idempotent      122
Identity      12
Image      13
Increasing filtration      26
Induced representation      182
Induced representation in the sense of Mackey      188
Inductive limit      5
Infinitesimal character      163
Infinitesimal Lie group      86
Inner automorphism      13 97
Integrable function      39
integral      39
Integral of a form      76
Integral orbit      239
Intertwining number      109
Intertwining operator      109
Invariant mean      129
Invariant subgroup      15
Inverse morphism      4
Inverse relation      2
Isomorphic Lie groups      99
Isomorphic objects      4
Isomorphism      4 13
Jacobson topology      147
Joint spectrum      47
k-irredicible      113
k-representation      226
Kazdan’s theorem      181
Kernel      13
Killing form      91
Kostant — Auslander theorem      241
Krein — Mil’man theorem      42
Lagrange distribution      246
Law of a composition      3
Left coset      15
Left fraction      152
Left G-space      13
Left Haar measure      130
Left ideal      25
Left K-module      28
Leray’s theorem      11
Lie algebra      86
Lie algebra, homomorphism      87
Lie group      83
Lie operator      73
Lie skew field      152
Lie’s theorem      90
Linear mapping      29
Linear operator      31
Linear representation      108
Linear representation of a Lie group      87
Linear space      31
Linearization of a projective representation      220
Linearly ordered set      2
Local coordinates      62
Locally convex space      36
Locally finite measure      39
Locally isomorphic Lie groups      99
Mackey’s criterion of inducibility      196
Mackey’s theorem      197
Manifold      62
Manifold with boundary      77
Maschke’s Theorem      140
Matrix element      135
Measurable function      39
Measurable set      38
Measurable vector function      57
Measure      38
Metric space      8
Minkowski functional      36
Mixed tensor      33
Modulus of a group      131
Monomial group      198
Monomial representation      182

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