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| Sagle A. A. — Introduction to Lie groups and Lie algebras |
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| Предметный указатель |
Manifold 40 41 43
Matrix ring or algebra 192 233
Maximal atlas 43
Maximal weight 327 329
Mean value theorem 17
Metric 3
Minimal polynomial 236
Models 284 304
Module 188 189
Multilinear map 20
Multiplication on homogeneous spaces 347
Multiplicative system 347
N(h) 265
Natural projection 97
Nilpoient radical 224 258
Nilpotent component of endomorphisms 237
Nilpotent endomorphisms 222 238
Nilpotent group 65 216 218 222
Nilpotent Lie algebra 66 219
Nilpotent Lie group 218
Nonassociative algebra 35 61 145 157 229 349
Nondegergerative form 57 228 231 236
Nonisotropic 231
Norirmalizer 265
Norm 3 194
Normal chart 124 129
Normal neighborhood 124
Normal subgroup 98 164
Normal typological group 96
Nucleus 92 108 109
O(N) 58
One-parameter group 80
One-parameter subgroup 119 120
open 3
Open ball 3 41
Open submanifold 41
operate 100
Orbit 100
Order of root system 288
Orthogonal complement 231
Orthogonal group 58
Outer automorphism 311
Paracompact 96
Parallel translation 339
Partial derivative 14
Path 168
Path connected 54
Positive definite symmetric bilinear form 2 58
Power associative 349
Product group 93
Product manifold 45
Projection map 74 76
Pseudo-Riemannian connection 341
Pseudo-Riemannian homogeneous space 341
Pseudo-Riemannian manifold 340
Pseudo-Riemannian structure 340
Quadratic algebras 196
Quaternion algebras 196
Quaternion numbers 197
Quotient algebra 152
Quotient group 98 152
Quotient module 189
Quotient topology 97
R(X) 158 191
R(X,Y),  340
rad G, rad g 207
Rad(A) 192
Radical 192 207 224 233 258
Rank of Lie algebra 265
Real analytic manifold 43
Real form 186 262 333
Real form of a representation 334
Real representation 333
Realification 185 262
Realization 185
Reductive 243 251
Reductive homogeneous space 165 343
Reductive pair, (G, H) or (g, h) 165
Regular element of a Lie algebra 265
Regular function 71 96 265 136
Representation 160 164 188
Restricted holonomy group 342
Riemannian structure 340
Right invariant metric 95
Right translation R(a) 91
Root spaces 268 278
Root system 284
Root system basis 288
| Roots 268 285
Schur's lemma 191 242 247
Second derivative 18
Seinidirect sum 206 255
Semisimple associative algebra 192 235
Semisimple component of an endomorphism 237
Semisimple endomorphism 236
Semisimple Lie algebra 192 207 250
Semisimple Lie group 207
Semisimple module 190 246
Semisimple nonassociative algebra 316
Senudirect product 93
Separation axioms 95 95
Signature of a Lie algebra 316
Simple Lie algeora 183 207
Simple Lie group 207 334
Simple module 190 246
Simple nonassociative algebra 191 232
Simply connected 136 170
Skew symmetric 13 60
SO(p, q), so(p, q) 59 185
Solvable group 202
Solvable Lie algebra 204 220
Solvable Lie group 203 210
Special linear algebra sl(V), sl(n, R), sl(n, K) 55 61 147 271 317
Special linear group SL(V), SL(n, R) 55 61 147
Special orthogonal algebra, SO(n) 59 61 147
Special orthogonal group, SO(n) 59 61 147
Special unitary algebra su(n) 61
Special unitary group SU(n) 61
Split composition algebra 197 199
Split erdomorphism 183 208 224
Split exact sequence 155
Split Lie algebra 183 264 316
Structure constants 182 301
Subgroup 97
Submanifold 49 70
Submersion 53 71
Submodule 153
Sup norm 5
Symmetric bilinear form 2 58
Symmetric neighborhood 92 103
Symmetric space 166
Symplectic algebra sp(n, R) 60
Symplectic group Sp(n, R) 60
T(M) 74
Tangent 62
Tangent bundle 74
Tangent map 69
Tangent vector 72
Taylor's formula 23
Taylor's series 125
Tensor product 178 190 261
Tensor product of algebras 180
Tensor product of homomorphisms 180
Tensor product of representations 330
Tf= Tf(p) = df(p) 68
Topological group 90
Topological manifold 41
Topological subgroup 97
Topological transformation group 100
Torsion tensor, Tor, Tor(X, Y) 340
Torus  45 99 104 139 155
Trace form 229 241
Trace tr T 9
Transitive 100
TRANSPOSE 38
Triangular matrices 65 201
U(n), u(n) 60
Uniform convergence 5
Unital module 193
Unitary group 60
Universal covering group 263
Usual coordinates 41
V* 66
Vector bundle 76
Vector field 78
Weight 327
Weight function 209
Weight space 208 270 327
Weight vector 208
Weyl basis 301 317
Weyl group-W 283 285 288
Weyl's formula 332 314
Weyl's theorem 283 245 250
Wrap around function 50 54
Z(G) 103 336
[x, y] 36 80
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