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| Porteous I.R. — Clifford Algebras and the Classical Groups |
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| Предметный указатель |
Hyperbolic 14
Hyperbolic plane 26
Hyperbolic plane, standard 23
Hyperplane at infinity 246
Ideal, left 11
Ideal, right 11
Idempotent 14
Idempotent, primitive 14
Image 1
Immersion 213 222
Immersive 213
Increment 209
Increment formula 211
INDEX 37
Index, Witt 37 109
Induced cover 197
Induced topology 193 196
Infinity, hyperplane at 246
Infinity, point at 111
Inflation 254
Injection 2
Injective 2
Injective criterion for smoothness 212
Inverse 2
Inverse function theorem 211
Inverse of a vector 24
inversion 254
Invertible vector 24
Involution of H 64
Involution, algebra 13
Involution, companion 266
Involution, grade 135
Involution, linear 5
Involution, main 135
Irreducible 15
Irreducible semi-linear map 95
Isomorphic quadratic spaces 26
Isomorphism, semi-linear 73
Isotropic quadratic space 23
Isotropy subgroup 21
Jacobi identity 242
Jacobian matrix 205
Jacobson, N. 277 286
James, I.M. 264 287
Jordan algebra 257
Juxtaposition 266
Kaplansky, I. 243 287
Kernel 3
Kernel of quadratic space 25
Kernel rank 3 51 73
Kervaire, M. 186 187 287
Kleinfeld, E. 186 187 287
Kuiper, N.H. 247 287
Lagrangian 112
Lawrynowicz, J., x 164 287
Left linear space 67
Left-coset exact 20 108 227
Leibniz notation 205
Length 39
Level set 1 212
Lie algebra 215 239 242
Lie bracket 239
Lie group ix 100 103 215 231
Lie group action 233
Lie group map 231
Lie group, exceptional 277
Line complex 79 113
Linear algebra 9
Linear map 2
Linear map, left 68
Linear map, right 68
Linear space 1 2 5
Linear space, left 67
Linear space, right 67
Linear subspace 3
Linear subspace of general linear group 164
Linked spheres 42
Liouville, J. 245 287
Liouville’s theorem 245
Lipschitz chart 176
Lipschitz group 141
Lipschitz, R. 176 287
Liverpool, the University of x
Locally Euclidean 215
Loos, O. 270 279 287
Lorentz group 238
Lounesto, P. ix 176
Main involution 135
Main involution of H 64
Majorana spinors 166
Maks, J. 167 172 255 287
Manifold, smooth 215 217
Manifold, Stiefel 244 262
Manifold, topological 215
MAP 1
Map, affine 6
Map, bilinear 4
Map, conformal 245
Map, Hopf 258 259
Map, identity 2
Map, linear 2
Map, Moebius 246
Map, orthogonal 25
Map, semi-linear 72
Matrix 3
Matrix algebra, full 9
Matrix, Jacobian 205
Matrix, quaternionic 69
Mean value theorem 211
Mennicke, J. 167 255 286
Meusnier, J.-B.-M.-C. 246 287
Micali, A. viii 287
Milnor, J. 186 187 287
Minimal left ideal 12 45 133
Module 5
Module map 5
Module,  5
Modulus of quaternion 60
Moebius group 248 255
Moebius map 246
Moebius transformation 250
Monoid 168
Montgomery, D. 283 287
Morton, H.R. 277
Motion, rigid 173 281
Moufang identities 190
Moufang, R. 190 287
Negative-definite 23
Neighbourhood 192
Neutral quadratic space 23
Neutral space 38
Non-degenerate correlation 25 52 74 98
Non-degenerate orthonormal subset 126
Non-degenerate quadratic form 25
Norm 191
Norm of quaternion 60
Norm, gradient 194
Norm, product 194
Norm, quadratic 145
Normed division algebra 179
North pole 40
Null quadratic space 23
Nullity 3
Octaves 180
Octonions 180
Open cover 197
Open map 196
Open set 191 192
Orbit 21
Orientation-preserving 7
| Orientation-reversing 7
Orthogonal complement 32
Orthogonal decomposition 32
Orthogonal group 27
Orthogonal group, special 27
Orthogonal isomorphism 26
Orthogonal map 25
Orthogonal quaternionic group 78
Orthogonal vectors 23
Orthonormal subset 126
Paige, L.J. 257 287
Paravector 140
Partition 1 195
Partner 10
Pauli algebra 152
Pentagon, rebracketing 2
Periodicity theorem for Clifford algebras 133
Pfaffian 175
Pfaffian chart 176
Pfaffian, complete 174
Physics x
Physics, theoretical 165
Pin group 146
Point at infinity 111
Pontrjagin, L.S. 238 243 287
Porteous, I.R. ix x 14 191 202 287 288
Positive-definite 23 55
Positive-definite correlated space 78
Power-associative 179
Preservation of angles 245
Primitive idempotent 14
PRODUCT 5
Product induced by correlation 74
Product norm 194
Product topology 196
Product, algebra 9
Product, cross 60
Product, direct 3
Product, Hermitian 52
Product, scalar 22
Product, tensor 81
Projection 3 196
Projection, stereographic 41 249
Projection, tangent 220
Projective compactification 246
Projective line 110
Projective line, Cayley 187
Projective plane 110
Projective plane, Cayley 187
Projective point 110
Projective quadric 112
Projective space 110
Pseudo-determinant 168
Pure part of quaternion 58
Pure quaternion 58
Quadratic form 22
Quadratic norm 22 145
Quadratic space, complex 49
Quadratic space, null 23
Quadratic space, real 23
Quadric Grassmannian 112
Quadric Grassmannian, affine 112
Quadric Grassmannians as coset spaces 116
Quadric, projective 112
Quasi-sphere 106 229 248
Quaternion product 58
Quaternion, pure 58
Quaternionic group 78
Quaternionic group, orthogonal 78
Quaternionic group, symplectic 78
Quaternions, algebra of 58
Quotient 195
Quotient topology 196
RADIUS 40
Radon — Hurwitz sequence 165
Radon, J. 165 288
Randriamihamison, L.-S. 164 288
Rank 3 51 73
Rank of quadratic space 25
Rank, kernel 3
Real part of quaternion 58
Real quadratic space 23
Reciprocity law 282
Recognition of subalgebras 88
Reducible anti-automorphism 15
Reducible automorphism 15
Reducible permutation 15
Reducible semi-linear map 95
Reflection 34
Reflection, hyperplane 34
Reflexive correlation 75 96
Reflexive scalar product 43
Rembielinski, j. 164 287
Representation, adjoint 238
Representation, Vahlen 254
reversion 135 162
Reversion of H 64
Reziprozitaetsgezetz 282
Right linear space 67
Rigid motion 173 281
Ring 5
Rotation 27 143
Rotation of  62
Rotation of  65
Samelson, H. 283 287
scalar 2
Scalar product, reflexive 43
Scalar product, skew 43
Scalar product, symmetric 22
Scalar triple product 61 182
Section 2
Segre, B. 13 288
Self-adjoint 53 75
Semi-linear map 51 72
Semi-linear maps over 94
Semi-neutral 112
Semi-neutral quadric Grassmannian 112
Semi-orientation-preserving 36
Semi-simple 277
Serras, H. x 285
Sesqui-linear 52 74
Shapiro, A. 124 285
Signature 37
Signature of correlated space 78
Signature of hermitian space 55
Signature theorem 36
Similar 14
SIMPLE 277
Skew 16 52
Skew correlation 74 95
Skew scalar product 43
Skew-adjoint 53 75
Skornyakov, L.A. 186
Smooth manifold 215 217
Smooth map 209 218
Smooth structure 216
Smooth submanifold 212
Smooth subset 212
Smooth, infinitely 209
Source 1
Source of a map 194
South pole 40
Space of half-spinors 134
Space of spinors 133
Space, linear 1 2 5
Special complex orthogonal group 50
Special linear group 7 99
Special orthogonal automorphism 27
Special orthogonal group 27
Special unitary automorphism 55
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