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Cohn P.M. — Lie Groups
Cohn P.M. — Lie Groups

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Название: Lie Groups

Автор: Cohn P.M.


The theory of Lie groups rests on three pillars: analysis, topology and algebra. Correspondingly it is possible to distinguish several phases, overlapping in some degree, in its development. It also allows one to regard the subject from different points of view, and it is the algebraic standpoint which has been chosen in this tract as the most suitable one for a first introduction to the subject. The aim has been to develop the beginnings of the theory of Lie groups, especially the fundamental theorems of Lie relating the group to its infinitesimal generators (the Lie algebra); this account occupies the first five chapters. Next to Lie's theorems in importance come the basic properties of subgroups and homomorphisms, and they form the content of Chapter VI. The final chapter, on the universal covering group, could perhaps be most easily dispensed with, but, it is hoped, justifies its existence by bringing back into circulation Schreier's elegant method of constructing covering groups.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1957

Количество страниц: 170

Добавлена в каталог: 16.12.2012

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Предметный указатель
Adjoint representation      135f.
Admissible chart      6
Analytic differential form      18 83
Analytic function      5 10
Analytic homeomorphism      21
Analytic infinitesimal transformation      17
Analytic isomorphism      49
Analytic manifold      6
Analytic mapping      20 23
Analytic structure      6
Analytic subgroup      51
Automorphism      61 132
Canonical chart, coordinates      56 109
Chart      4
Commutator      60
Compatible      30
Composition function      44
coordinates      4
Covering homomorphism, group      145ff.
Differential      15
Differential form      16 82
DIMENSION      4 12 46
Discrete space      9
Dual space, basis      13
Effective      66
Endomorphism      132
Exponential mapping      76
Exterior algebra      80
Exterior differentiation      84
functor      20
Germ      42
Grassmann algebra      90
Homogeneous space      32
Homomorphism of Lie algebras      127
Homotopic      142
Ideal      128
Identity component      39
Induced mapping, topology, etc.      36ff.
Infinitesimal transformation      16 65
Inner product      13
Invertible mapping      23
Isomorphism of Lie algebras      61
Jacobi identity      60
Kernel of a homomorphism      127
Left-invariant      64 87
Lie algebra      60 64
Lie group      44
Lie product      60
Linear form      13
Local analytic homomorphism      72
Local analytic isomorphism      49
Local cross-section      127
Local Group      41
Local isomorphism      43
Local Lie group      48
Locally Euclidean      5
Loop      140
Manifold      5
Maurer — Cartan equations      96
Maurer — Cartan equations, form      87
Maurer — Cartan equations, relations      92
Natural mapping, homomorphism      30 128
Nucleus      33 41
Open mapping      37
Path, path-connected      140f.
Pfaffian form      82
Product manifold      29
Quotient algebra      128
Representation      135ff.
Simply connected      144
Structure constants      65
Subalgebra      68
Submanifold      25
Symbol of infinitesimal transformation      18
Tangent vector      11
Topological group      30
Topological isomorphism      38 41
Torus      8f. 39
Transformation function      63
Transformation group      66
Translation      31 62
Universal covering group      139 152
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