Postnikov M. — Lectures in Geometry. Semestr V. Lie Groups and Lie Algebras :: Электронная библиотека попечительского совета мехмата МГУ

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Postnikov M. — Lectures in Geometry. Semestr V. Lie Groups and Lie Algebras

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Название: Lectures in Geometry. Semestr V. Lie Groups and Lie Algebras

Автор: Postnikov M.

Аннотация:

This textbook like the rest of the series is compiled from lectures delivered by the author to students at Moscow State University. The audience was made up of final year students and postgraduates, and as a consequence, a certain level of knowledge (for example, the properties of manifolds) is assumed.

Язык:

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 440

Добавлена в каталог: 02.05.2010

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Предметный указатель

$G_{2}$       301
Ado theorem      207
Algebra, $Z_{2}$ -graded      251
Algebra, alternative      293
Algebra, associative      44
Algebra, associative, algebraic element of      408
Algebra, free      98
Algebra, in noncommuting unknowns      98
Algebra, invertible element of      44
Algebra, Jordan      323
Algebra, normed      288
Algebra, of double numbers      256
Algebra, of dual numbers      256
Algebra, of octaves (of Cayley numbers)      293
Algebra, of polynomials      98
Algebra, over a field      43
Algebra, universal enveloping      104
Antiautomorphism of an algebra, involutory      258
Associator      307
Cain group      393
Campbell — Hausdorff series      76
Campbell — Hausdorff series, in the Dynkin form      124
Cartan theorem      136 202 231
Cartan’s criterion, for semisimplicity      374
Cartan’s criterion, for solvability      365 368
Casimir operator      375
Categories, equivalent      131
Categories, of coverings      181
Category, of coverings      170
Category, of pointed coverings      171
Cayley algebra      293
Cayley construction      22
Cayley image, of a group      22
Cayley image, of a matrix      20
Cayley number      293
Centre, of a Lie algebra      349
Centre, of an associative algebra      258
Chart, canonical      93
Clifford algebra      249
Clifford algebra, element of, even      251
Clifford algebra, odd      251
Clifford group of degree and index $\varepsilon$       259
Coalgebra      114
Coamalgam      165 173 176
Coboundary      379
Cochain      377
Cocycle      379
Coidentity      114
Commutator Lie algebra      60
Commutator of two elements of an associative algebra      60
Component of arcwise connectedness      27
Comultiplication      114
Configuration, $F_{4}$       343
Conjugation, of a Clifford algebra      258
Conjugation, of a finite-dimensional algebra over $\mathbb{R}$       286
Constants, structural      298
Coordinates, canonical      93
Coordinates, canonical, of the first kind      94
Coordinates, canonical, of the second kind      94
Coordinates, normal      83
Covering      159
Covering, pointed      165
Covering, pointed, maximal      172
Covering, pointed, simply connected      172
Covering, pointed, universal      172
Covering, smooth      183
Covering, trivial      168
Covering, weak      160
Coverings, pointed equivalent      172
Curve of a vector field, integral      36
Curve of a vector field, integral, maximal      36
Decomposition of a representation into a direct sum      383
Degree, of a linear operator, external th      283
Degree, of a monomial      99
Diagonal mapping      114
Differentiation of an algebra      61
Differentiation of an algebra, interior      61
Differentiations, adjoint      333
Doubling of an algebra      286
Dynkin polynomial      78
Dynkin’s Theorem      123
Element, primitive      114
Element, special      108
Engel theorem      354
Extension of Lie algebras      388
Extension of Lie algebras, central      419
Extension of Lie algebras, trivial      388
Factor group, local      140
Fibering, induced      144
Fitting decomposition of a linear operator      383
Freudenthal theorem      333
Friedrichs’ theorem      118
Frobenius theorem      148
Frobenius theorem, generalized      295
Function in an algebra, derived      47
Function in an algebra, exponential      47
Functional, bilinear invariant      360
Functional, Killing’s      361
Functor, completely univalent      142
Functors, quasi-inverse      131
Germ, of homomorphisms      69
Germ, of local Lie groups      68
Graph of the Pfaffian system      145
Group covering      189
Group, admitting the Cayley construction      22
Group, algebraic      232
Group, fundamental      192
Group, local, embeddable      204
Group, local, globalizable      204
Group, locally flat      97
Group, of unimodular unitary matrices      32
Group, orthogonal symplectic      24
Group, simply-connected covering      196
Group, smooth      15
Group, symplectic      26
Group, topological      16
Group, topological, without small subgroups      96
Group, unitary      25
Group, unitary, symplectic      26
Group,real linear symplectic      23
Hausdorff (separable) topological space      16
Homomorphism, continuous      16
Homomorphism, local      160
Homomorphism, of algebras      43
Homomorphism, of Lie groups, smooth      15
Homomorphism, of local Lie groups      69
Hopf algebra      114
Ideal of a Lie algebra      138
Ideal of a Lie algebra, characteristic      406
Idempotent      324
Idempotent, primitive      324
Identity      67
Identity element      67
Identity, of elasticity      307
Immersion      228
Integral of a Pfaffian system      144
Isomorphism of topological groups, local      194
Jacobi identity      60
Jacobson theorem      352
Jordan decomposition of a linear operator      366
Killing’s functional      361
Kronecker product of matrices      276
Lagrange theorem      254
Leibnitz formula      233
Levi theorem      391
Lie algebra      60
Lie algebra, $f_{4}$       330
Lie algebra, $g_{2}$       296
Lie algebra, abelian      349
Lie algebra, free      98

Lie algebra, linear      351
Lie algebra, linear, irreducible      356
Lie algebra, nilpotent      349
Lie algebra, of a Lie group      63
Lie algebra, of a local group      69
Lie algebra, of vector fields on a manifold      62
Lie algebra, realizable      418
Lie algebra, reductive      357
Lie algebra, semisimple      348
Lie algebra, simple      392
Lie algebra, solvable      347
Lie bracket      60
Lie bracket, of vector fields      62
Lie correspondence      136 209
Lie functor      41 66 70 130
Lie group      15
Lie group $F_{2}$       330
Lie group $G_{2}$       296
Lie group algebra      129
Lie group, local      67
Lie group, local, analytic      142
Lie group, smooth      142
Lie groups, equivalent local      68
Lie groups, locally isomorphic      66
Lie monomial      120
Lie nilsubalgebra      351
Lie polynomial      76 100
Lie subgroup      209
Lie’s third theorem      133
Linearization      306
Local factor group      140
Local group, embeddable      204
Local group, globalizable      204
Local Lie group      67
Local Lie group, analytic      142
Local Lie group, smooth      142
Local Lie groups, equivalent      68
Local subgroups      134
Local subgroups, invariant      138
Local subgroups, locally flat      135
Localization functor      69
Manifold, integral      210
Manifold, maximal      212
Manifold, parallelizable      35
Mapping, smooth      17
Matrix algebra      44
Matrix function, exponential      47
Matrix Lie group      51
Matrix representations, equivalent      275
Matrix, complex orthogonal      25
Matrix, complex symplectic      25
Matrix, hermitian      322
Matrix, J-orthogonal      23
Matrix, J-skew-symmetric      23
Matrix, J-unitary      25
Matrix, monomial      276
Matrix, nonexceptional      20
Matrix, octave, skew — Hermitian      331
Matrix, symplectic      22
Matrix, unitary      25
Metric algebra      288
Module over a Lie algebra      103
Monomial      99
Monomial, empty      99
Morphism, of coverings      170
Morphism, of Lie groups      15
Moufang identity, central      314
Moufang identity, right      315
Neighbourhood, canonical      93
Neighbourhood, normal      74
Nilradical of a Lie algebra      351
Nilrepresentation of a Lie algebra      412
Norm in an algebra, multiplicative      45
Object of a category, initial      248
Octave      293
One-parameter subgroup      38
Part, of a linear operator, diagonalizable      366
Part, of a linear operator, nilpotent      366
Part, of a local group      68
Path      27
Plane, projective octave      326
Poinar $\acute{e}$ — Birkhoff theorem      111
Poincar $\acute{e}$ group      192
Polarization      306
Polynomial, noncommutative      76
Problem, Hilbert’s fifth      97
Product, left internal      282
Product, of ideals      403
Product, right internal      283
Property, of being universal      104
Property, of naturalness      73
Quotient algebra of a Lie algebra mod an ideal      140
Quotient manifold      239
Radical of a Lie algebra      348
Radical of a Lie algebra, nilpotent      359
Rank of a smooth mapping      214
Representation, of a Lie algebra      364
Representation, of a Lie algebra, adjoint      364
Representation, of a Lie group, adjoint      86
Representation, semispinor      280
Restriction      145
Shift, left      19
Shift, right      19
Shifts by an element       19
Solenoid (group), irrational      208
Space, arcwise connected topological      27
Space, connected topological      27
Space, homogeneous      239
Space, locally (arcwise) connected topological      27
Space, locally simply connected topological      185
Space, of a representation of a Lie algebra      364
Space, pointed topological      165
Space, semilocally simply connected topological      173
Space, simply connected topological      169
Spinor group of degree and index $\varepsilon$       259
Spinor representation      280
Square, dissected      218
Square, universal      165
Subalgebras of an algebra      44
Subcategory, complete      44
Subfibering, completely integrate      151
Subfibering, involutory      151
Subfibering, of a tangent fibering (or bundle)      145
Subgroup, discrete      194
Subgroup, invariant      209
Subgroup, of a Lie group      209
Subgroup, possessing an In-image      58
Subgroups, invariant local      138
Subgroups, locally flat local      135
Submanifold      208
Subset, evenly covered by a mapping      159
Subset, locally closed      230
Subset, of a group, small      198
Subset, of the product of two groups, distinguished      198
Subspace (subalgebra), associatively nilpotent      351
System, integrable      144
System, pfaffian      143
Tensor product, of $Z_{2}$ -graded algebras, skew      253
Tensor product, of algebras      113
Tensor product, of vector spaces      112
Trace functional, of a Lie algebra      360
Trace functional, of a representation of a Lie algebra      364
Triplicity principle, for group Spin (8)      316
Triplicity principle, infinitesimal      316
Triproduct, scalar      329
Unit sphere      20
Variety, algebraic      232
Vector field, complete      37
Vector field, on a group, left invariant      34
Vector field, on a manifold      33

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