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Hausner M., Schwartz J.T. — Lie groups, Lie algebras
Hausner M., Schwartz J.T. — Lie groups, Lie algebras

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Название: Lie groups, Lie algebras

Авторы: Hausner M., Schwartz J.T.


A large number of mathematical books begin as lecture notes; but, since mathematicians are busy, and since the labor required to bring lecture notes up to the level of perfection which authors and the public demand of formally published books is very considerable, it follows that an even larger number of lecture notes make the transition to book form only after great delay or not at all. The present lecture note series aims to fill the resulting gap. It will consist of reprinted lecture notes, edited at least to a satisfactory level of completeness and intelligibility, though not necessarily to the perfection which is expected of a book. In addition to lecture notes, the series will include volumes of collected reprints of journal articles as current developments indicate, and mixed volumes including both notes and reprints.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1968

Количество страниц: 239

Добавлена в каталог: 09.07.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
Предметный указатель
A(n)      58—59
Ad $\lambda$      66
Adjoint of an operator      6
Adjoint representation      94
Analytic functions of an operator      10—11
Automorphisms, Canonical factorization      181
Automorphisms, Diagonalization      198
Automorphisms, Jordan canonical form      194
Baker — Hausdorff theorem      see Campbell — Baker — Hausdorff theorem
Bilinear form      1
Campbell — Baker — Hausdorff theorem      68
Cartan criterion      98—99
Cartan subalgebra      95
Cartan subalgebra isomorphisms      138
Casimir operator      144
Chromosome      120
Classical algebras, models      123—125
Classical algebras, real forms      184—201
Classical groups      81—85
Closed subgroups      77
Commutative algebra      77
Compact groups      220—226
Complexification      87
Component of identity      38
Conjugations, definition      173
Conjugations, equivalence      176
Conjugations, in Algebras of type A${}_{n-1}$      184—187
Conjugations, in Algebras of type B${}_{m}$, C${}_{m}$, D${}_{m}$      188— 193
Conjugations, in E${}_{6}$      207—213
Conjugations, in E${}_{7}$      205—207
Conjugations, in E${}_{8}$      202—205
Conjugations, in F${}_{4}$      213—214
Conjugations, in G${}_{2}$      201—202
Conjugations, positive      176
Connected group      37
Coordinates, definition      20
Coordinates, for functions      21
Coordinates, for tangent vectors      25
Covering group      42
Covering space      14—19
Derivative of a curve      29—30
Diagonalization      4
Differential equations      32
Dynkin diagram      120—121
Eigenspace      5
Eigenvalue, analytic dependence      10
Eigenvalue, definition      5
Eigenvector      5
Exceptional algebras      122
Exceptional algebras, models      126—136
Exceptional algebras, real forms      201—220
Exponential function      60
Factor algebra      see Quotient algebra
Factor group      see Quotient group
Fundamental group, definition      14
Fundamental group, of a covering space      16
Fundamental group, of a Lie group      42
Germ      44
Gl(n)      58—59
Hermitian form      1
Hermitian operator      7
Homeomorphism      22
Homomorphism, of fundamental groups      14
Homomorphism, of Lie algebras      55
Homomorphism, of Lie algebras, differentiability      64
Homomorphism, of Lie algebras, induced by group homomorphism      56
Homomorphism, of Lie groups      38
Homomorphism, of Lie groups, defined by local homomorphism      39
Homomorphism, of Lie groups, induced by algebra homomorphism      70
Homotopy      13
Ideal, definitions      73 88
Ideal, induced by invariant subgroups      74
Implicit function theorem      12 28—29
Inner automorphism      138
Integrability conditions      56
Invariant measure      19
Invariant subgroup      73
Invariant subspace      142
Irreducible invariant subspace      143
Isomorphism, of Lie algebras      55
Isomorphism, of Lie groups      38
Isomorphism, of Lie groups, induced by algebra isomorphism      71
Isomorphism, of Lie groups, induced by local isomorphism      41
Isomorphism, of Lie groups, induced by mapping of roots      108
Jacobian      27
Lie algebra      55 86
Lie bracket, definition      50
Lie bracket, induced in a subalgebra      72
Lie group      37
Local homomorphism      38
Local isomorphism, definition      38
Local isomorphism, induced by algebra isomorphism      71
Local isomorphism, inducing global isomorphism      41
Local subgroup      44
Logarithmic coordinate system      64
Manifold      20
Natural bilinear form      94
Neighbors      114
Nilpotent algebra      88 92
Non-singular bilinear form      2
Non-singular subspace      3
O(n) (orthogonal group)      83
Positive definite form      4
Positive definite operator      8
Product manifold      32
Quotient algebra, definition      74
Quotient algebra, determined by quotient group      75
Quotient group, definition      43 75
Quotient group, determining quotient algebra      75
Radical      160
Radical splitting theorem      160—163
Regular map      34
Representations, definition      87
Representations, equivalence      146
Root space      94
Roots, definition      94
Roots, positive      106
Roots, simple set      105
Semi-direct product of groups      165
Semi-direct sum of algebras      159 163
Semi-simple algebra, characterized as a direct sum of simple algebras      99
Semi-simple algebra, characterized by natural bilinear form      94
Semi-simple algebra, characterized by root structure      122
Semi-simple algebra, definition      93
Signature      5
Simple algebra, characterized by root structure      115
Simple algebra, definition      93
Simple algebra, models      123—136
Simple algebra, real forms      215
Simply connected space      13 16
Singular bilinear form      2
Skew-symmetric bilinear form      2
SL(n) (Special linear group)      81
Solvable algebra      88
Sp(n) (Symplectic group)      84
Special linear group      see SL(n)
Spectrum      5
Subalgebra      72
Subgroup, definition      44
Subgroup, induced by subalgebra      72
Submanifold      34
Symmetric bilinear form      1
Symplectic group      see Sp(n)
Tangent vector, coordinates      25
Tangent vector, definition      23
Tangent vector, on submanifold      35
Topological group      19
Total commutativity      196
Unitary space      6
Vector field      31
Weight space      87 90
Weight vector      87
Weights      87 88 146
Weyl group      140
Weyl reflection      140
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