|
|
Авторизация |
|
|
Поиск по указателям |
|
|
|
|
|
|
|
|
|
|
Postnikov M. — Lectures in Geometry. Semestr V. Lie Groups and Lie Algebras |
|
|
Предметный указатель |
301
Ado theorem 207
Algebra, -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 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, 343
Conjugation, of a Clifford algebra 258
Conjugation, of a finite-dimensional algebra over 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, 330
Lie algebra, 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 330
Lie group 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 — Birkhoff theorem 111
Poincar 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 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 -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
|
|
|
Реклама |
|
|
|