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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 groupsАвторы: 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: Рубрика: Математика /Серия: Сделано в холле Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1997Количество страниц: 242Добавлена в каталог: 17.03.2011Операции: Положить на полку |
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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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