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| Porteous I.R. — Clifford Algebras and the Classical Groups |
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| Предметный указатель |
Absolute value of quaternion 60
Action, Clifford 257
Action, spinor 257
Adams, J.F. x 186 187 285
Adjoint 27 53 96 101
Adjoint representation 238
Admissible chart 217
Affine form 112
Affine map 6
Affine space 6
Affine subspace 6 212
Ahlfors, L 167 176 254 285
Algebra anti-isomorphism 9
Algebra isomorphism 9
Algebra map 9
Algebra, alternative 179
Algebra, Cayley ix 180
Algebra, Clifford 123
Algebra, division 178
Algebra, extensive 138
Algebra, exterior 138
Algebra, geometric 123
Algebra, Grassmann 138
Algebra, Jordan 257
Algebra, Lie 239 242
Algebra, linear 9
Algebra, Pauli 152
Algebra, tensor 124
Algebra-reversing map 9
Alternative algebra 179
Analytic 209
Angle, absolute 39
Angles, preservation of 245
Annihilator, dual 4
Annihilator, orthogonal 32
Anti-automorphism of H 62
Anti-automorphism, algebra 13
Anti-involution of H 64
Anti-involution, algebra 13
Anti-rotation 27 143
Arnol’d, V.I. 66 112 285
Artin, E. x 176 285
Atiyah, M.F. x 124 285
Atlas 215
Atlas, standard 111
Automorphism of H 62
Automorphism, algebra 13
Automorphism, linear 3 5
Automorphism, orthogonal 27
Automorphism, triality 267
Axis of rotation 35
Banach space 202
Basis 2
Basis theorem for  -linear spaces 92
Basis theorem for hermitian spaces 54
Basis theorem for real quadratic spaces 34
Basis theorem for symmetric correlated quaternionic spaces 77
Benn, I.M. 166 285
Bijection 2
Bijective 2
Bilinear map 4
Biquaternions 174
Bivector 176
Bott, R. 124 186 187 285 287
Boudet, R. x 287
Boundary point 192
bounded linear map 194
Boyer, R.H. x
Brack, R.H. 186 188 285
Bracket, Lie 239
Brackx, F. x 285
Bredon, G.E. 277 285
Bundle, tangent 219 220
Cartan, E. 247 256 278 285
Cauchy — Schwarz inequality 39
Cayley algebra, ix 180
Cayley chart 118 174
Cayley heptagon 185
Cayley numbers 165
Cayley projective line 187
Cayley projective plane 187
Cayley triangle 184
Cayley, A. 180 286
Centre 40
Centre of algebra 10
Chain rule 203 207
Chart 176 215
Chart, admissible 217
Chart, Cayley 118 174
Chart, Pfaffian 176
Chart, standard 111 215
Charts on quadric Grassmannians 114
Chevalley, C. 124 243 286
Chisholm, J.S.R. x 286
Choice, axiom of 2
Circle group 56 57
Circle, unit 40
Classical group 100 103
Classification theorem for -correlations 98
Classification theorem for -semi-linear maps 94
Classification theorem for complex quadratic spaces 49
Classification theorem for complex symplectic spaces 50
Classification theorem for hermitian spaces 55
Classification theorem for real symplectic spaces 47
Classification theorem for symmetric correlated quaternionic spaces 78
Classification theorem of real quadratic spaces, first part 34
Classification theorem of real quadratic spaces, second part 36
Clifford action 257
Clifford algebra, complex 134
Clifford algebra, even 136
Clifford algebra, real 123
Clifford embedding 262
Clifford group 141
Clifford homogeneous space 262
Clifford matrix 167
Clifford, W.K. 123 286
Closed map 196
Closed set 192
Cnops, J. 164 167 168 172 255 286
Code numbers for ten types of classical group 103
Code numbers for ten types of matrix algebra with anti-involution 155
Coimage 1
Common, A.K. x 286
Commutative diagram 19
Compact space 198
Compactification, conformal 247
Compactification, projective 246
companion 267
Companion involution 266
Complement, linear 3
Complement, orthogonal 32
Complex field, as real algebra 9
Complex group = symplectic group 79
Complex orthogonal group 50
Complex quadratic space 49
Complex Stiefel manifold 265
Complex symplectic plane 50
Complex symplectic space 50
Complexification 86 105
Composite 1
Conformal compactification 247
Conformal group 248
Conformal map 245
Conformal spheres 248
Conformal transformation, special 252
Conjugate of a quaternion 59
Conjugation 135 148
Conjugation anti-involution 59
Connected 199
Continuous map 193
| Continuously differentiable map 205
contour 1
Contraction Lemma 211
Correlated -space 95
Correlated linear space 24
Correlated quaternionic space 74
Correlation 52 74
Correlation, linear 24
Correlation, semi-linear 95
Correlation, symmetric 24
Coset space representation 20
Cover, double 146
Cover, induced 197
Cover, open 197
Cross product 60
Decomposition, orthogonal 32
Decomposition, Witt 37 109
Delanghe, R. viii 285
Determinant 6 98
Determinant, absolute 70
Diagram chasing 18
Diffeomorphism 211 218
Differentiable map 205
Differential of a map 205
Differential, higher-order 209
DIMENSION 2
Dimension of affine subspace 212
Dimension of classical group 103
Dimension of Grassmannian 111
Dimension of smooth manifold 217
Dimension of submanifold 212
Dimension, quaternionic 68
Dirac spinors 165
Direct product 3
Direct sum 3
Disconnected 199
Dissimilar 14
Distance 39 192
Division algebra 178
Division algebra, normed 179
Domain 1
Double cover 146
Double field 5 91
Double field , as real algebra 9
Dual 52
Dual annihilator 4
Dual linear map 4
Dual linear space 4
Dual of semi-linear map 73 95
Dual, linear 68
Elstrodt, J. 167 255 286
Embedding 196 213
Embedding, Clifford 262
Endomorphism, linear 5
Epstein, D.B.A. 264 276 288
Equation of map 2
Equivalent atlases 216
Equivalent correlations 52
Equivalent norms 194
Equivalent semi-linear correlations 74 95
Equivalent smooth manifolds 217
Euclidean space 39
Euclidean, locally 215
Even Clifford algebra 136
Exact pair 18
Exact sequence 18
Exact sequence, short 18
Exact, left-coset 20 108
Existence theorem for Clifford algebras 131
Extensive algebra 138
Exterior algebra 138
Fibre 1 212
Field 2
Field, complex 2
Field, double 5 91
Field, real 2
Fillmore, J. 167 255 286
Finite-dimensional 2
Five 154
Form induced by correlation 74
Form, Hermitian 52
Form, quadratic 22
Form, sesqui-linear 95
Free, linearly 92
Freudenthal, H. 278 286
Freudenthal’s principle of triality 278
Frobenius, G. 186
Fuchs, L. 13 286
General linear group 7 98
General linear group, thought of as a unitary group 91
Generators, set of 12
Geometric algebra 123
Gilmore, R. 243 277 286
Grade involution 135
Gradient norm 194
Grassmann algebra 138
Grassmann, H. 138 286
Grassmannian 110
Grassmannian, quadric 112
Grassmannians as coset spaces 113
Graves, J. 180 286
Group  ix 270
Group action 21
Group action, Lie 233
Group map = group homomorphism 20
Group map, Lie 231
Group map, topological 225
Group, circle 56 57
Group, classical 100 103
Group, Clifford 141
Group, complex orthogonal 50
Group, conformal 248
Group, general linear 7 98
Group, Lie viii 100 103 231
Group, linear 7
Group, Lipschitz 141
Group, Lorentz 238
Group, Moebius 248 255
Group, orthogonal 27
Group, Pin 146
Group, quaternionic 78
Group, real symplectic 47
Group, special linear 7 99
Group, special unitary 55
Group, spin 146
Group, topological 225
Group, unitary 55 104
Grunewald, F. 167 255 286
Haantjes, J. 246 286
Half-spinor space 134
Hamilton triangle 183
Hamilton, Sir W.R. 58 286
Hampson, A. ix 286
Hausdorff space 192
Heine — Borel theorem 197
Helgason, S. 243 277 286
Helmstetter, J. x 287
Heptagon, Cayley 185
Hermann, R. 247 286
Hermitian form 52
Hermitian product 52
Hermitian space 52
Higher-order differential 209
Homeomorphism 193
Homogeneous space 226
Homogeneous space, Clifford 262
Hopf map 111 258 259
Hopf, H. 122 286
Hurwitz pair 164
Hurwitz, A. 164 165 186 286
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