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Gorbatsevich V.V., Vinberg E.B., Onishchik A.L. — Foundations of Lie theory and Lie transformation groups
Gorbatsevich V.V., Vinberg E.B., Onishchik A.L. — Foundations of Lie theory and Lie transformation groups

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Название: Foundations of Lie theory and Lie transformation groups

Авторы: Gorbatsevich V.V., Vinberg E.B., Onishchik A.L.

Аннотация:

From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" The New Zealand Mathematical Society Newsletter


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 242

Добавлена в каталог: 17.03.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
A-structure      114
Absolute value      74
Action of a group      100
Action of a group by Inner automorphisms      103
Action of a group by left translations      103
Action of a group by right translations      103
Action of a group by two sided translations      103
Action of a group, asystatic      124
Action of a group, effective      101
Action of a group, free      106
Action of a group, left      100
Action of a group, linear      102
Action of a group, primitive      124
Action of a group, right      100
Action of a group, simply transitive      106
Action of a group, systatic      124
Action of a group, transitive      103
Action of a group, trivial      100
Action of a Lie algebra      211
Action of a Lie algebra, locally primitive      212
Action of a Lie algebra, locally transitive      212
Action of a Lie algebra, primitive      212
Action of a Lie algebra, transitive      212
Action of a Lie group      12 100
Action of a Lie group, affine      12
Action of a Lie group, asystatic      124
Action of a Lie group, irreducible      140
Action of a Lie group, linear      12
Action of a Lie group, linear compact      108
Action of a Lie group, local      104
Action of a Lie group, local globalizable      105
Action of a Lie group, locally effective      101
Action of a Lie group, minimal      220
Action of a Lie group, primitive      124
Action of a Lie group, proper      149
Action of a Lie group, regular      195
Algebra, Banach      82
Algebra, Bol      91
Algebra, Heisenberg      50
Algebra, Hopf      66
Algebra, Lie      32
Algebra, Lie, free      70
Algebra, Lie, nilpotent      58
Algebra, Lie, semisimple      57
Algebra, Lie, solvable      56
Algebra, Maltsev      91
Algebra, Moufang — Lie      91
Algebra, universal enveloping      60
Algebra, Weyl      65
Auslander, L.      169
Betti, E.      167
Bialgebra      66
Birkhoff, G.      61
Bochner, S.      114 115
Bol, G.      88 91
Borel, A.      152
Bundle      115
Bundle of A-structures      218
Bundle of positive densities      117
Bundle, associated      117
Bundle, Borel      194
Bundle, frame      116
Bundle, homogeneous      129
Bundle, Hopf      122
Bundle, induced      119
Bundle, Karpelevich — Mostow      136
Bundle, locally trivial      15
Bundle, Mostow      168
Bundle, natural      190
Bundle, principal      116
Bundle, structure      197
Bundle, tautological      120
Bundle, Tits      174
Bundle, trivial      15 116
Bundle, universal      120
Campbell, J.E.      59 71
Canonical coordinates of the first kind      45
Canonical coordinates of the second kind      45
Cartan, E.      47 87 218
Cayley, A.      89
Central series decreasing of a Lie algebra      58
Central series decreasing of a Lie group      58
Centralizer of a Lie subgroup      40
Centralizer of an element of a Lie algebra      36
Centre of a Lie algebra      40
Centre of a Lie group      40
Commensurability of groups      198
Commensurability of groups, weak      198
Commutator (ideal) mutual of ideals      55
Commutator (subalgebra) of a Lie algebra      52
Commutator (subgroup) mutual of normal subgroups      55
Commutator (subgroup) of a Lie group      52
Commutator higher of a Lie algebra      56
Commutator higher of a Lie group      56
Commutator of vector fields      111
Component of a homogeneous manifold, almost simply connected      203
Component of a homogeneous manifold, semisimple      203
Component of a homogeneous manifold, solvable      203
Comultiplication      71
Corank of a manifold      129
Coxeter, H.      127
Decomposable manifold      219
Deformation of a path      40
Dense winding of the torus      14
Derivation of a Lie algebra Interior      50
Derivation of an algebra      35
Diagonal map      66
Differential of a homomorphism of Lie groups      32
Differential of an action of a Lie group      34
Differential of the exponential mapping      46
Differential operator right Invariant      67
Dimension, Cohomological      200
Dimension, Gelfand — Kirillov      65
Dimension, virtual      200
Direction vector of a one-parameter subgroup      44
Duflo, M.      64
Dynkin, E.B.      72
Element almost invariant      102
Element invariant      100
Element regular of a compact Lie group      153
Element regular, of a tangent algebra      153
Element representative      102
Element singular of a compact Lie group      153
Enlargement of an action      102
Enlargement of an action, natural      139
Enlargement of an action, of type I      145
Enlargement of an action, of type II      145
Enlargement of an action, radical      178
Euler characteristic of a group      201
Euler characteristic, of a manifold      129
Exponential mapping      45 77
Extension of structure group      116
f-projectable field      110
Factorization of a group      138
Factorization of a Lie group      141
Factorization of a Lie group, global      142
Factorization of a Lie group, irreducible      143
Factorization of a Lie group, maximal      178
Factorization of a Lie group, trivial      143
Factorization, of a Lie algebra      148
Fibre bundle      115
Fibre of a bundle      115
Fixed point      100
Flag manifold      148
Flow      102
Flow, local      108
Formal group law      78
Frechet, M.      84 135
Frobenius, F.      131
Function representative      107
Functor Lie      29 79
G-bundle      118
G-bundle, homogeneous      129
G-bundle, trivial      119
G-space      101
G-space, analytic      101
G-space, differentiable      101
G-space, equiorbital      151
G-space, topological      101
Gauge transformation      82
Gelfand, I.M.      64 65
Geodesic loop      89
Gleason, A.      88
Globalization of a local action      105
Goldie, A.W.      64
Grassmann, H.G.      120
Group formal      78
Group formal, Isotropy      105
Group of components of a Lie group      22
Group of covering transformations      26
Group of flows      81
Group of interior automorphisms of a Lie algebra      49
Group of interior automorphisms of a Lie group      49
Group of transformations      101
Group, isotropy, linear      106
Group, Lie      6
Group, Lie — Frechet      84
Group, Lie — Frechet tame      85
Group, Lie, abelian      43
Group, Lie, abelian complex      43
Group, Lie, abelian real      43
Group, Lie, aspherical      204
Group, Lie, Banach (Hilbert)      81
Group, Lie, complex      6
Group, Lie, linear      8
Group, Lie, local      11
Group, Lie, nilpotent      58
Group, Lie, of transformations      101
Group, Lie, of type (I)      171
Group, Lie, p-adic      75
Group, Lie, semi-simple      204
Group, Lie, solvable      56
Group, Lie, standard      76
Group, Lie, universal covering      26
Group, Lie, vector      7
Group, loop      81
Group, model      121
Group, semi-simple      214
Group, topological      86
Group, virtually torsion free      200
Group, Wang      169
Hausdorff, F.      59 71
Heisenberg, W.      50
Helgason, S.      46
Hilbert, D.      74 87 88 156
Hirsch, K.A.      201
Homogeneous manifold      123
Homomorphism of formal groups      78
Homomorphism of Lie groups      9
Homomorphism of Lie groups, covering      24
Homotopical characteristic      129
Hopf, H.      122
ILB-group (strong)      86
ILH-group (strong)      86
Inclusion of actions      102
Inclusion of actions, improper      102
Inclusion of actions, proper      102
Isomorphic actions      101
Isomorphic actions, local Lie groups      11
Isomorphism of group actions      101
Isomorphism of homogeneous bundles      130
Isomorphism of Lie groups      9
Iwasawa Manifold      161
Iwasawa, K.      161
Jacobi identity      32
Jacobi, C.      32
Karpelevich, F.I.      136
Kernel non-effectiveness      101
Kernel non-effectiveness of action      101
Killing, W.      183
Kirillov, A.A.      64 65
Klein model      121
Klein, F.      121 170
Koszul, J.-L.      150
Kreck, M.      186 193
Largest nilpotent ideal      58
Largest nilpotent ideal, normal Lie subgroup      59
Levi, E.E.      137
Lie bracket      111
Lie bracket, derivative      109
Lie, S.      4 6 86 99 103 111 210 212 214
Lifting of an action      155
Linear isotropy representation      106
Linear isotropy representation, representation of a Lie group      9
Linearlization of an action      103
Lobachevski, N.I.      134
Localization of an action      104
Locally isomorphic Lie algebra actions      211
Locally isomorphic Lie groups      11
Locally isomorphic local actions of Lie groups      211
Locally isomorphic triples of Lie groups      141
Locally similar actions of Lie algebras      211
Locally similar local actions of Lie groups      211
Locally similar subalgebras of the Lie algebra of vector fields      211
Loop      88
Loop, alternative      89
Loop, analytic      89
Loop, Bol      88
Loop, disassociative      89
Loop, local      89
Loop, monoassociative      89
Loop, Moufang      89
Maltsev closure      53
Maltsev, A.I.      53 88 91 161
Manifold homogeneously decomposable      219
Mann, L.N.      154
Mapping equivariant      101
Mikhailichenko, G.G.      216
Milovanov, M.B.      170
Moebius, A.      164
Montgomery, D.      88 114 115 147 149 150 153 179
Morphism of actions      101
Morphism of homogeneous bundles      130
Morphism of local actions      104
Mostow, G.D.      136 137 149 166 218
Moufang, Ruth      89 91
Multiplication      66
Myers, S.B.      115
Nilmanifold      160
Norm      74
Norm, non-Archimedean      74
Norm, ultrametric      74
Normalizer of a subspace in an algebra      37
Normed field      74
Normed non-archimedean field      74
Number Coxeter      127
Number of ends of a group      202
One-paremeter subgroup      44
Orbit      105
Orbit, exceptional      153
Orbit, principal      153
Orbit, singular      153
Ore, O.      64
Ostrowski, A.      75
Palais, R.S.      149
Part of a fundamental group semi-simple      200
Part of a fundamental group solvable      200
Path      37
Peter, F.      156
Poincare polynomial      126
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