404 Index

classical compact groups, 136

closed, 344

closed set, 208

coadjoint orbit, 1

cochain, cocycle, coboundary, 217

cocycle equation, 22, 218, 372, 388

coeﬃcients, 338

cohomology group, 217

commutant, 352

commutative

diagram, 213

Fourier analysis, 135

commutator, 270

compact real form, 314

compatible, 374, 385

complete, 209, 338

completion, 210

complexification, 315

composition, 212

connected space, 208

continuous basis, 46

continuous map, 208

continuous sum, 351

contractible chart, 232

contraction, 292

countable additivity, 386

covariance condition, 330

covector field, 241

Coxeter element, 307

Coxeter number, 147

creation operators, 40

cross-norm, 341

curvature form, 13

cyclic vector, 15, 346

de Rham cohomology, 221

decomposable, 351

deformation (of a Lie algebra), 292

degenerate series, 180

derivation, 241

of degree k, 251

diagonalizable, 352

diamond Lie algebra, 43, 126

diffeomorphic, 232

diffeomorphism, 232

differential

k-form, 241

1-form, 241

direct

integral, 351

of algebras, 352

limit, 222

product, 215

sum, 214

direct product, 320

direct sum, 361

directed set, 222

disjoint measures, 350

distance, 208

divergence, 250

division algebra, 272

domain of definition, 343

natural, 43

dominant weight, 246

dual cone, 300

dual hypergroups, 195

dual root, 312

dual root system, 312

Dynkin diagram, 302

Dynkin graph, 302

extended, 144

effective, 319

Einstein’s rule, 242

elementary cell, 204

elementary system, 197

equivalent

atlases, 231

deformations, 292

essential homomorphism, 236

essentially self-adjoint, 344

Euler-Bernoulli triangle, 191

exceptional groups, 136

exponential, 109

coordinate system, 282

exponential coordinates, 33

exponential map, 283

exponents, 307

extension, 297, 344

central, 297

trivial, 297

exterior point, 208

factor manifold, 229

factorization problem, 200

faithful, 319

fiber, 238, 239

fiber bundle, 238

base of, 238

section of, 239

fibered product, 170

over G, 320

field of geometric objects, 243

filtration, 149

first amendment to Rule 2, 124

first integral, 267

fixed point, 320

flag, 149

flag manifold, 149, 323

degenerate, 149

Fourier analysis, 135

Fourier coeﬃcients, 364