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Onishchik A.L. (ed.) — Lie Groups and Lie Algebras (volume 1)
Onishchik A.L. (ed.) — Lie Groups and Lie Algebras (volume 1)

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Название: Lie Groups and Lie Algebras (volume 1)

Автор: Onishchik A.L. (ed.)

Аннотация:

The book by Gorbatsevich, Onishchik and Vinberg is the first in a series of volumes devoted to the theory of Lie groups and Lie algebras. The first part of the book deals with the foundations of the theory based on the classical global approach of Chevalley followed by an exposition of the alternative approach via the universal algebra and the Campbell-Hausdorff formula. It also contains a survey of certain generalizations of Lie groups. The second more advanced part treats the topic of Lie transformation groups covering e.g. properties of orbits and stabilizers, homogeneous fibre bundles, Frobenius duality, groups of automorphisms of geometric structures, Lie algebras of vector fields and the existence of slices. The work of the last decades including the most recent research results is covered. The book contains numerous examples and describes connections with topology, differential geometry, analysis and applications. It will be of great interest to graduate students and researchers in mathematics and theoretical physics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 235

Добавлена в каталог: 09.06.2006

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 translation      103
Action of a group by two deled translations      103
Action of a group, affine      12
Action of a group, asystatic      124
Action of a group, asystatlc      124
Action of a group, effective      101
Action of a group, free      10
Action of a group, Irreducible      140
Action of a group, left      100
Action of a group, linear      12
Action of a group, linear compact      108
Action of a group, local      104
Action of a group, local global isable      106
Action of a group, locally primitive      212
Action of a group, locally transitive      212
Action of a group, locbiiy effective      101
Action of a group, minimal      220
Action of a group, primitive      124
Action of a group, proper      149
Action of a group, regular      105
Action of a group, right      100
Action of a group, simply transitive      100
Action of a group, systatlc      124
Action of a group, transitive      212
Action of a group, trivial      100
Action of a Lie algebra      2
Action of a Lie group      12 100
Algebra, Bol      91
Algebra, Heisenberg      60
Algebra, Hopf      00
Algebra, Lie      32
Algebra, Maltsev      91
Algebra, Maltsev free      70
Algebra, Maltsev nilpotent      68
Algebra, Maltsev semisimple      67
Algebra, Maltsev solvable      66
Algebra, Moufang — Lie      91
Algebra, Uanach      82
Algebra, universal enveloping      60
Algebra, Weyl      66
Auslander, L.      169
Betti. E      167
Bialgebra      00
Birkhoff. G      61
Bochner, S.      114 115
Bol, G      88 91
Borel. A      152
Bundle      116
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      130
Bundle, locally trivial      16
Bundle, natural      190
Bundle, principal      116
Bundle, structure      197
Bundle, tautological      120
Bundle, Tita      174
Bundle, trivial      15 116
Bundle, universal      120
Campbell, J. E.      59 71
Canonical coordinates of the first kind      46
Canonical coordinates of the second kind      46
Cartan E.      47 87 216
Central series, algebra      68
Central series, decreasing of a Lie group      68
Centraliser an element of a Lie algebra      36
Centraliser of a Lie subgroup      40
Centre of a Lie algebra      40
Centre of group      40
Commensurability of group      196
Commensurability of weak      196
Commutator mutual of a Lie algebra      62
Commutator mutual of a Lie group      66
Commutator mutual of ideals      55
Commutator mutual of mutual of normal subgroups      65
Commutator mutual of vector fields      111
Commutator mutual, higher of a Lie algebra      66
Component of a homogeneous manifold, almost simply connected      203
Component of a homogeneous manifold, semsimple      203
Component of a homogeneous manifold, solvable      203
Comultiplication      71
Corank of a manifold      129
Coxeter, II      127
Coy Icy, A.      86
Decomposable manifold      219
Deformation of a path      40
Dense winding of the torus      14
Derivation of a Lie algebra Interior      60
Derivation of an algebra      36
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, Celfand — Kiriuov      66
Dimension, cohoinologlcal      200
Dimension, virtual      200
Dirction vector of a one-parameter subgroup      44
Duflo, M.      64
Dynkin, E. B.      72
Element almost invariant      102
Element almost invariant of a tangent algebra      153
Element almost invariant, invariant      100
Element almost invariant, regular of a compact Lie group      163
Element almost invariant, ropr native      102
Element almost invariant, singular of a compact Lie group      153
Eniarg ment of an action      102
Eniarg ment of an action, natural      139
Eniarg ment of type II      146
Eniarg ment, radical      178
Euler characteristic of a group      201
Euler characteristic of a manifold      129
Exponential mapping      46 77
Extension of structure group      110
Factorisation of a group      138
Factorisation of a Lie algebra      148
Factorisation of a Lie group      141
Factorisation of a Lie group, global      142
Fibre bundle      115
Fibre bundle of a bun die      115
Fixed point      100
Flag manifold      148
Flow      102
Flow, local      108
Formal group law      78
Frlchet, M.      84 135
Frobcniufl, 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      161
G-space, topological      101
Gauge transformation      82
Gelfand, I. M.      64 65
Geodesic loop      89
Gleason, A.      88
Globalisation of a local action      106
Goldie, A W.      64
Grassmann, H. G.      120
Group formal      78
Group formal, abelian      43
Group formal, Isotropy      106
Group formal, Isotropy, linear      106
Group Lie of transformations      101
Group Lie of type (I)      171
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, nil potent      68
Group Lie, semi-slmple      204
Group Lie, solvable      56
Group Lie, standard      76
Group Lie, universal covering      26
Group Lie, vector      7
Group of a Lie group      49
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      40
Group of transformations      101
Group, abelian complex      43
Group, chet      84
Group, Lie      6
Group, Lie — Fr      4
Group, Lie — Frichet tame      86
Group, loop      81
Group, model      121
Group, sem-simple      214
Group, topological      86
Group, virtually torsion free      200
Group, Wang      169
Hausdorff, F.      69 71
Heisenberg, W.      50
Helguon, S.      46
Hilbert, D.      74 87 88 156
Hirsch, K. A.      201
Homogeneous manifold      123
Homomorphism of formal group      78
Homomorphism of Lie group      9
Homomorphism of Lie group, covering      24
Homotoplcal characteristic      128
Hopf, H.      122
ILB-group (strong)      86
Inclusion of actions      102
Inclusion, improper      102
Inclusion, proper      102
Isomorphic actions      101
Isomorphic, local Lie groups      11
Isomorphism of group actions      101
Isomorphism of homogeneous bundle      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 of action      101
Killing. W      183
Kirillov, A. A.      64 68
Klein model      121
Klein, F.      121 170
Kotftul, J — L      150
Kreck, M.      186 193
Largest nilpotent ideal      68
Largest, normal He subgroup      60
Levi, E. E.      137
Lie bracket      111
Lie derivative      100
Lie, S.      4f 6 86 99 03 111 210 212 214
Lifting of an action      166
Linear isotropy representation      106
Linear, representation of a Lie group      0
Linearization of an action      103
Lobaduvski, N. I.      134
Localisation of an action      104
Locally isomorphic Lia algebra actions      211
Locally isomorphic Lia algebra actions, Lie groups      11
Locally isomorphic Lia algebra actions, local actions of Lie groups      211
Locally isomorphic Lia algebra actions, triples of Lie groups      141
Locally similar actions of Lie algebras      211
Locally similar actions of Lie algebras, local actions of Lie groups      211
Locally similar actions of Lie algebras, subalgebras of the Lie algebra of vector fields      211
Loop      88
Loop, alternative      80
Loop, analytic      86
Loop, Bol      88
Loop, disassociative      80
Loop, local      80
Loop, monoassociative      80
Loop, Moufang      80
Maltsev closure      63
Maltsev, A.      1 53 88 91 161
Manifold homogeneously decomposable      210
Mann, L. N.      164
Mapping equivariant      101
Milovanov, M. B.      170
Mlkhaillchenko, G. G.      216
Montgomery D.      88 114
Morphism of actions      101
Morphism of homogeneous bundles      130
Morphism of local actions      104
Mostow, Cr D.      136 137
Moufang, Ruth      89 91
Mttbius, A.      164
Multiplication      66
Myers, S. B.      16
Nilmanifokl      160
Nonfiallser of a subspace in an algebra      37
Norm      74
Norm, non-archlmedean      74
Norm, ultrametric      74
Normed fit id      74
Number Coxeter      127
Number Coxeter of ends of a group      202
One-paremeter subgroup      44
Orbit      06
Orbit, exceptional      163
Orbit, principal      163
Orbit, singular      163
Ore      64
Ostrowski, A.      75
Palais, R. S.      140
Part of a fundamental group semi-simple      200
Part of a fundamental group semi-simple, solvable      200
Path      37
Petere F      166
Poincaxi Polynomial      126
Poincaxi Polynomial, series      126
Polncart, H.      59 61
Pontryagln, L. S.      88 169
Postnikov, N, N.      29 193
Primitive element of a bialgebra      66
Product, direct of Lie groups      7
Product, fibred      117
Product, semi-direct      20
Projection map of a fibre bundle      116
Pseudoorthogonal matrix      23
Pseudounttary matrix      23
Quotient group Lie      17
Quotient group Lie map      16
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