Price J.F. — Lie groups and compact groups :: Электронная библиотека попечительского совета мехмата МГУ

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Price J.F. — Lie groups and compact groups

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Название: Lie groups and compact groups

Автор: Price J.F.

Аннотация:

The theory of Lie groups is a very active part of mathematics and it is the twofold aim of these notes to provide a self-contained introduction to the subject and to make results about the structure of Lie groups and compact groups available to a wide audience. Particular emphasis is placed upon results and techniques which explicate the interplay between a Lie group and its Lie algebra, and, in keeping with current trends, a coordinate-free notation is used. Much of the general theory is illustrated by examples and exercises involving specific Lie groups.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1977

Количество страниц: 177

Добавлена в каталог: 21.10.2010

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Предметный указатель

$\Gamma$ (dual object)      165
1-parameter subgroup      34
AD      88
Adjoint representation      88 106
Algebra      59
Algebra free      59
Algebra Lie      17
Analytic atlas      7
Analytic atlas, equivalent      45
Analytic diffeomorphism      7
Analytic diffeomorphism, local      40
Analytic function      4
Analytic homeomorphism      7
Analytic homomorphism      43
Analytic manifold      7
Analytic map      7
Atlas      2
Atlas 0-dimensional      2
Atlas analytic      7
Atlas compatible      25
Atlas generators of an      6
Atlas maximal      6
Atlas smooth      6
Automorphism group (Aut(L))      126
Campbell — Baker — Hausdorff (CBH) formula      61 65
Cartan's criterion for semi-simplicity      124
Cartan's criterion for semi-solubility      158
Central function      167
Centre      110
Chart      1
Chart trivializing      12
Circle group (T)      27
Compact group      165
Compact group, Lie algebra      122 128
Compact group, Lie group      115
Compact Lie group      136
Compatible atlas      25
Complete (metric space)      82
Covering group      75
Curve (analytic)      80
Curve (analytic), broken      80
Curve (analytic), coincident      91
Curve (analytic), length of      80
Derivation      16
Derivation, local      23
Derivation, of a Lie algebra $(\partial(L))$       125
Derivative      2
Derivative, directional      16
Derivative, Frechet      4
Derivative, partial      32
Diffeomorphism      7
Diffeomorphism, analytic      7
Differentiable map, function      2
Dimension of a manifold      2
Dimention of a manifold, Lie group      25
Direct product      42
Direct product, Lie algebra of      112
Distance metric (d(p, q))      81
Dual object $(\Gamma)$       165
Embedding      20
Exponential map      39
Exponential map, power series      47
Form, invariant      123
Form, Killing      123
Frechet derivative      4
Free algebra      59
Function, analytic      5
Function, differentiable      2
Function, smooth      3
Gel'fand — Ralkov theorem      163
General affine group (GA(E))      56
General linear      25 46
General linear group (GL(E))      26 46
Geodesic      84 91
Group, circle      27
Group, compact      165
Group, exceptional      137
Group, general affine      56
Group, Lie      25
Group, locally compact      161
Group, orthogonal      2 7
Group, profinlte      158
Group, special linear      54
Group, special orthogonal      27
Group, special unitary      27
Group, spinor      138
Group, sporadic      153
Group, symplectic      137 46
Group, torsion      156
Group, unitary      27
Haar integral, measure      167
Homeomorphism, analytic      7
Homeomorphism, local analytic      40
Homomorphism, local      56 73
Hypergroup      115 166
Ideal      106
Identity component      28
Immersion      13
Inner derivatit n      125
Invariant metric      8 7
Inverse limit      139
Inverse limit, mapping system      139
Inverse limit, mapping theorem      40

Isometry      87
Jacobi's identity      17
Killing form      123
Killing form, essential uniqueness of      157
Killing form, nondegenerate      124
Left invariant vector field      31
Length      83
Length, invariance of      99
Length, reparametrization by      99
Lie algebra      17
Lie algebra, commutative      77
Lie algebra, compact      122 128
Lie algebra, nilpotent      100
Lie algebra, of a Lie group      39
Lie algebra, of a product      112
Lie algebra, semisimple      121
Lie algebra, simple      121
Lie algebra, soluble      158
Lie group      25
Lie group, 0-dimensional      119
Lie group, 1-dimensional      78 119
Lie group, 2-dimensional      119
Lie group, abelian      77
Lie group, compact      115
Lie group, dimension of      25
Lie group, linear      119
Lie group, semisimple      121
Lie group, simple      121
Lie group, simply connected      72
Lie homomorphism, isomorphism      43 50
Lie product      14 17
Lie product, multiple      61
Lie subalgebra, subgroup      43 50
Linear Lie group      119
local      90
Local homomorphism      56 73
Local homomorphism, isomorphism      73
Manifold      2
Manifold derivative      12
Manifold,       18
Manifold, 0-dimensional      2
Manifold, analytic      7
Manifold, dimension of      2
Manifold, infinite-dimensional      19
Manifold, Riemannian      80
Manifold, smooth      6
Metric      81
Metric, invariant      87
Metric, Riemannian      80
Natural projection for tangent bundle $(\pi)$       11
Nilpotent Lie algebra      100
No small subgroups      41 115
Normal subgroup      106
Open mapping theorem      161
Orthogonal group (O(n))      27
Orthogonal group, special (SO(n))      27
Partial derivative      32
Path connected      72
Product, direct      42 140 161
Profinite group      158
Projective limit      139 159
Rank      12
Representation      162
Representation, adjoint      88 106
Representation, conjugate      165
Representation, irreducible      115 163
Riemannian manifold      80
Riemannian manifold, invariant      87
Riemannian manifold, metric      80 82
Semisimple Lie algebra, group      121
Simple Lie algebra, group      121
Simply connected      72
Small subgroups      41
Smooth atlas      6
Smooth atlas, function      3
Smooth atlas, manifold      6
Smooth atlas, map      7
Special (SU(n))      27
Special linear group (SL{E))      54
Special orthogonal group (SP(n))      27
Special unitary group (SU(n))      27
Structure theorems      132 136 145
Subgroup, 1-parameter      34
Subgroup, closed      27 69
Subgroup, Lie      101
Subgroup, normal      106
Symplectic group (Sp(n))      137
Tangent bundle (T(M))      10
Tangent bundle (T(M)), natural projection for      11
Tangent bundle (T(M)), trivial      20
Tangent space       10
Taylor's formula      5
Taylor's formula, for Lie groups      62
Topological group      160
Torsion group      156
Torus       27
Translation operator       29 31
Trigonometric polynomial      167
Unitary group (U(n))      27
Vector field      13
Vector, analytic      13
Vector, left invariant      31
Vector, related      37

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