406 Index
Lie algebra (continued)
graded, 249
nilpotent, 297
semisimple, 297
solvable, 297
Lie bracket, 248
Lie derivative, 248
Lie group, 269
locally isomorphic, 269, 284
matrix, 269
Lie superalgebra, 249, 289
limit of the sequence, 208
linear continuous functionals, 335
linear geometric objects of first order, 245
linear order, 300
linear relations, 344
local coordinates, 228, 231
locally projective structure, 22
logarithm map, 194
loop group, 187
Lorentz transformation, 181
manifold
k-smooth n-dimensional, 231
abstract, 230
algebraic, 236
algebraic, degree of, 262
analytic, 231
complex, 235
ahler, 150, 261
non-orientable, 234
oriented, 233
Poisson, 263
quotient, 229
reduced, 266
reduced symplectic, 169
separable, 231
smooth, 231
smooth, structure of, 232
symplectic, 256
map
m-smooth, 232
Master equation, 372
matrix element, 358
matrix notation, 269
maximal torus, 323
mean value property, 46
measure
equivalent, 349
disjoint, 350
projector-valued, 385
quasi-invariant, 52
spectral, 350
metaplectic group, 184
metric space, 209
metrizable, 209
mirror, 299
modified
Rule 1, 124
Rule 10, 134
Rule 2, 111, 131
Rule 6, 114
Rule 7, 118
Rule 8, 134
module
projective, 243
moduli space, 235
moment map, 17, 267
morphism, 212
multiplicity, 165, 346, 349
multiplicity function, 350
multiplicity of the weight, 165
multiset, 165
n-th homotopy group, 216
natural
bundle, 326
domain of definition, 344
Hilbert space, 379
operation, 247
negatively related charts, 233
neighborhood, 208
Nelson condition, 42
Nijenhuis bracket, 251
nilpotency class, 72
nilpotent
Lie algebra, 71
Lie group, 72
non-degenerate, 374, 384
non-homogeneous form for cochains, 218
norm, 335
normal, 340
normal real form, 314
normalized, 173
normalizer, 322
object, 212
couniversal, 214
final, 214
geometric, 243
initial, 214
representing, 215
universal, 214
octonion, 146
odd symplectic group, 28, 182
open set, 208
operator
adjoint, 335
compact, 341
dual, 335
Hilbert-Schmidt, 341
irreducible, 363
smoothing, 366
unbounded, 343
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