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Rosenfeld B. — Geometry of Lie Groups
Rosenfeld B. — Geometry of Lie Groups

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Название: Geometry of Lie Groups

Автор: Rosenfeld B.

Аннотация:

This book represents the fruits of the author's many years of research and teaching. The introductory chapter contains the necessary background information from algebra, topology, and geometry of real spaces. Chapter 1 presents more specialized information on associative and nonassociative algebras and on Lie groups and algebras. In Chapters 2 through 6 geometric interpretations of all simple Lie groups of classes An, Bn, Cn, and Dn as well as of finite groups of Lie type are given. In Chapters 5 and 6 geometric interpretations of quasisimple and r-quasisimple Lie groups of the same classes are included. In Chapter 7, for the first time ever, geometric interpretations of all simple and quasisimple Lie groups of exceptional classes G2, F4, E6, E7, and E8 are given. The role of exercises is played by the assertions and theorems given without a full proof, but with the indication that they can be proved analogously to already proved theorems. Audience: The book will be of interest to graduate students and researchers in mathematics and physics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 393

Добавлена в каталог: 18.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$i-\frac{1}{2}$ — Plane      160
$\alpha_{i}$-figure, $\alpha_{i_{1}},..., \alpha_{i_{k}}$-figure      102
(n + 2) - Spherical coordinates      206
(n — p) - Hedral angle      195
Absolute, bi — Hermitian conic      343
Absolute, complex      311 313
Absolute, differential      17
Absolute, Hermitian conic      335—336 340—341
Absolute, hyperquadric      220—221 223—224
Absolute, null-system      311 313
Absolutes, of quasielliptic, quasihyperbolic etc. spaces      285—286
Absolutes, of r-quasielliptic, r-quasihyperbolic, etc. spaces      292
Absolutes, of symmetric spaces      271
Absorption law      6
Addition of velocities in the Special Relativity      216
Additivity      197
Adjacent lines and points      108 118
Adjoint, group of a Lie group      80
Adjoint, matrix      41
Adjoint, representation      93
Affine, connection      18
Affine, coordinates      7 108
Affine, parameter      19
Affine, rotation      123
Affine, space      7 107
Affine, transformation      26 122 166
Affine, Weyl group      75
Albert theorem      45 56
Albert — Kalish theorem      89
Algebra      4
Algebra, structure      107
Algebraic, complex      152
Algebraic, congruence      152
Almost complex, split complex structure      332
Alternativity      54
Alternion      48
Analytic manifold      15
Analytic point      8 114
Angle between, hypercycles      298
Angle between, hyperspheres      189
Angular defect, excess      197
Annihilator      38
Anticyclic number      35
Antiholomorphic real 2—direction      183 241 339
Antimotion      176
Antisimilitude      176
Antisymmetry axiom      6
Arithmetic Fuchsian group      268
Arm of a couple of vectors      199
Associative law      6 9
Asymptotic direction      136—137
Autodual configuration      155
Automorphism      3 32—33 45—46
Autopolar simplex      147 229 251 296
Axial space      287 322
Basis vectors      4
Beltrami interpretation      232
Betti numbers      85
Bi — Hermitian conic      343
Bialtemion      52
Bicomplex number      34
BICUBE      71
Bioctonion      56
Bioctonionic Hermitian plane      340—341
Biparabolic space      105
Biquasisimple algebra      38
Biquatemion      48
Block      7
Borel subgroup      101
Brauer — Weyl theorem      52
Canonical form of a system of sliding vectors      201
Cartan, algorithm      81 240
Cartan, matrix      68
Cartan, subalgebra, subgroup      62
Cartan, theorem on simple associative algebras      45
Cartan, theorems on exceptional Lie groups      333 340
Cauchy inequality      9
Cauchy — Riemann conditions      33
Cayley number      54
Cayley — Dickson number      55
cell      115
Cellular decomposition, polynomial      115
Center of a hyperquadric      137 296
Center of a hypersphere      10 188 252
Center of a system of sliding vectors      200
CHARACTER      81
circle      11
Circular transformation      204 299
Classification of conics in hyperbolic plane      257—259
Classification of hyperquadrics      259
Clifford algebra, number      48
Clifford quadric      253
Clifford theorems      208—209
Closed subsets, closure      5
Co — Euclidean space      284
Cocube      71
Coefficient of connectedness      75
Collineation      27 125 167 334
Commutative law      6 8
Commutator      23
Comotion      304
Compact space      6
Complete quadrangle, quadrilateral      155
Complex, chain      157
Complex, Lie group      61 71
Complex, number      29
Conformal, configuration      207
Conformal, interpretations of a quadratic space      231
Conformal, space      11 204
Conformal, transformation      27 299
Congruence of m-planes      111 152
Conjugate, diameters      138
Conjugate, elements      29—31 34 40 43 47 49 51 55—56
Connected space      5
Connectedness group      95
Constant, curvature      222
Constant, holomorphic curvature      248
Continuous, mapping      6
Continuous, space      5
Contravariant vector      12
Convolution      12
Coordinates of vectors      4
Copseudo — Euclidean space      284
Correlation      126
Cosymmetry figure      159 304
Couple of vectors      199
Covariant, derivative      16
Covariant, vector (covector)      12
Coxeter, diagram      71—75
Coxeter, number      65
Coxeter, theorem on regular honeycombs in hyperbolic space      267
Coxeter, transformation      72
Cross ratio      127
Cross ratio, pairs      133
cube      71
Cubeable figure      194
Cubic surface with      27
Cubic surface with rectilinear generators      72 151
Curl      14
Curvature of space      219 223 336
Curvature tensor      16
Cyclic number      35
De Vries symbol      155
Derivative of vector function      14
Desargues, configuration      155
Desargues, theorem      110 119
Determinant      41 386
Diameter of hyperquadric      137
Diametral, hyperplane      138 1
Diametral, m-plane      137
Differentiable manifold, vector function      14
Dihedral angle      195
Direct sum, product      3
Discrete space      5
Distance      8 220
Distributive, lattice      6
Distributive, law      8
Divergence      14
Diverging lines      108
Division algebra      4
dodecahedron      71
Dodecahedron, spaces      280—281
Dominant weight      94
Dual, configurations      155
Dual, Lie group      61
Dual, number      31
Duality and stability      328—330
Duality principle      70 135 260
Duocomplex number      34
Duodual number      34
Duooctonion      60
Duoquaternion      48
Dycomplex number      34
Dydual number      34
Dynamical screw      201
Dynkin diagram, theorem      67
Dyoctonion      60
Dyparabolic space      55
Dyquaternion      48
Edge of a polyhedron      184
Eighth-octonion      61
Einstein rule      4
Elastic algebra      91
Elasticity      329
electromagnetic field      217
Ellipsoid      139
Elliptic and hyperbolic, lines of kind a      299
Elliptic and hyperbolic, regular polyhedra      266
Elliptic and hyperbolic, spaces      219 222
Endomorphism      3
Equidistant, barrel      253
Equidistant, hyperquadric      252 254
Equivalent systems of sliding vectors      199 202
Euclidean space      8 168—169
Even-dimensional quadratic symplectic space      313
Event      216
Exponents of a simple Lie group      73
Extended, Dynkin diagram      74
Extended, hyperbolic space      222 225
Extended, pseudoelliptic, pseudohyperbolic space      222 225
Exterior, differential form      20
Exterior, power of a linear representation      96
Exterior, product of vectors      13
Fermi coordinates      235
Field      2
Finite, affine space      161
Finite, conformal space      213
Finite, geometries with exceptional fundamental groups      368
Finite, Hermitian space      282
Finite, projective space      161
Finite, pseudoconformal space      213
Finite, quadratic space      282
Finite, symplectic space      326—327
Flag      103 295
Flag, manifold      103
Flag, plane      32 288
Flag, space      295
Focal variety      111
Free, module      106
Free, vector      198
Freudenthal, algebra      91
Freudenthal, magic square      350
Freudenthal, theorems on metasymplectic geometries      352 366
Frobenius algebra      38
Fuchsian groups      267—268
Fundamental, figures in a space with exceptional fundamental group      356—366
Fundamental, figures in a space with simple fundamental group      102
Fundamental, group      25
Fundamental, linear representations      94 367
Fundamental, root vectors      67
G-elliptic $\sigma$-space      331
G-pseudoelliptic, G-pseudohyperbolic $\sigma$—spaces      332
G-quasielliptic, G-quasihyperbolic etc $\sigma$—spaces      333
Galilean space      288
Galois, field      2
Galois, group      69
Gauss — Bonnet theorem      17
General linear group      22
Generalized coordinates, momenta      327
Geodesic      15
Geodesic, curvature      17
Geographical coordinates      193
Gorbunova theorem      305
Gradient      14
Grassmann, algebra      53
Grassmann, coordinates      103
Grassmann, manifold      121
Grassmannian      151
Group, algebra      37
Halfhyperplane, halfline, halfplane, halfpoint      160
Halfspace      160 184
Hamiltonian canonical equations      327
harmonic oscillator      328—329
Hausdorff space      5
Heisenberg group      255—256 313
Hermitian in a finite space      165
Hermitian, conic      354
Hermitian, ellipsoid, hyperboloid, paraboloid      139
Hermitian, elliptic interpretation of projective, symplectic geometry      237 316
Hermitian, Euclidean space      169
Hermitian, form      169
Hermitian, hyperquadric      136
Hermitian, hypersphere      188
Hermitian, linear congruence of lines      114
Hermitian, null-system      153
Hermitian, symplectic space      313
Hesse, configuration      155
Hesse, interpretation      239
Hjelmslev, algebra      38
Hjelmslev, space      109
Holomorphic plane      183
Holomorphy, angle      182 339
Holomorphy, vector      183 339
Homeomorphism      6
Homogeneous space      25
Homomorphism      2
Homothety      27
Hurwitz theorem      40 55
Hyperbolic, Coxeter diagram      268
Hyperbolic, regular polyhedron      266
Hyperbolic, space      219 222
Hypercone      140
Hypercubic      151
Hypercycle      297
Hypercylinder      140
Hyperplane      7 108
Hyperplane at infinity      7
Hyperquadric      136
Hyperquadric in a finite space      163—165
Hyperquartic      151
Hypersphere      10 188
Ibnal — Haytham — Lambert quadrangle      262
icosahedron      71
Ideal      3
Ideal point      11 114
Idempotent      30
Imprimitive group      25
Incidence structure      7
Incident fundamental, parabolic figures      100
Index of a pseudo — Euclidean space      10
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