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| Авторизация |
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| Baker A. — Matrix Groups: An Introduction to Lie Group Theory |
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| Предметный указатель |
Minimal polynomial 52
Negative light cone 158
Negative root 293
Non-degenerate inner product 227
Non-trivial root 279
Norm 5—7 33 111
Norm, complete 10
Norm, operator 6 34
Norm, supremum 6
Normaliser 260
Normed algebra 111
Null root space 279
Null vector 158
One-parameter group 57
One-parameter semigroup 57
One-parameter subgroup 57
Open disc 7
Operator norm 6 34
Orbit 37
Orthogonal 90
Orthogonal complement 274
Orthogonal group 20
Orthogonal group, special 21
Orthogonal idempotent 104
Orthogonal matrix 20
Outer automorphism 124
Outer automorphism, group 124
Parabolic subgroup 221
Past pointing light cone 158
Path, component 241
Path, connected 235
Path, connected, locally 235
Permutation matrix 153
Permutation matrix, generalised 132
Pfaffian 156 232
Phase portrait 635
Pinor group 143
Polynomial, homogeneous 38
Polynomial, minimal 52
Positive definite 87
Positive definite, inner product 228
Positive light cone 158
Positive root 293
Principal bundle 214
Product, cross 68
Product, direct 19 71 101
Product, inner 227
Product, semi-direct 19 71
Product, topology 11
Product, vector 68
Projective linear group 125 219
Projective quaternionic symplectic group 219
Projective space 217
Projective special unitary group 219
Projective unitary group 219
Proper Lie ideal 69
Pure quaternion 119
Quadratic form 227
Quasi-symplectic group 233
Quaternion, pure 119
Quaternion, real 119
Quaternionic conjugate 120
Quaternionic conjugation 120
Quaternionic symplectic group 121
Quaternionic symplectic group, projective 219
Quaternions, skew field of 118
Quotient, Lie algebra 70
Quotient, topology 33 212
Quotient, topology, universal property of 213
Real Clifford algebra 130
Real inner product 86
Real part 138
Real quaternion 119
Real symmetric bilinear form 87
Real symplectic group 27
Reduced determinant 116
Reduced echelon form 226
Reduced root system 292
Reflection, hyperplane 291
Reflection, in a hyperplane 23
Related inner products 227
Related symmetric matrices 227
Representation 38
Representation, adjoint 75
Representation, left regular 103
Right multiplication map 187
Ring anti-homomorphism 120
Root 279 292
Root, fundamental 292
Root, negative 293
Root, non-trivial 279
Root, positive 293
Root, simple 292 293
Root, space 279
| Root, space, decomposition 280
Root, space, null 279
Root, system 292
Root, system, dual 301
Root, system, reduced 292
Rotation 22
Semi-direct product of groups 19
Semi-direct product of Lie algebras 71
Semi-simple algebra 106
Semi-simple Lie group 276
Semigroup, one-parameter 57
Separable 182
SIMPLE 70
Simple algebra 104
Simple coroot 300
Simple Lie algebra 70
Simple Lie group 274
Simple root 292 293
Skew field 100
Skew hermitian 83
Skew symmetric 26
Skew symmetric form 229
Smooth action 208
Smooth curve 183
Smooth manifold 181 182
Smooth map 181 182
Space, Hausdorff 14
Space, homogeneous 214
Space, projective 217
Spacelike vector 158
Special linear group 5
Special orthogonal group 21
Special unitary group 28
Special unitary group, projective 219
Sphere, unit 144
Spinor group 144
Stabiliser 37
Standard torus 252
Strictly upper triangular 81
Subalgebra, commutator 69
Subalgebra, derived 69
Subalgebra, Lie 69
Subfield, central 102
Subgroup, Borel 18
Subgroup, generated by a subset 144
Subgroup, Lie 187
Subgroup, matrix 15 16
Subgroup, one-parameter 57
Subgroup, translation 19
Subgroup, unipotent 18
Subgroup, upper triangular 18
Submanifold 186
Subset, clopen 17
Subset, closed 8
Supremum norm 6
Symmetric group 153
Symmetric matrices, related 227
Symmetric real bilinear form 87
Symmetric skew 26
Symplectic form 26 229
Symplectic geometry 26
Symplectic group 27 121
Symplectic group, quaternionic 121
Symplectic group, real 27
Tangent space 71 184
Timelike vector 158
Topological generator 206 254
Topological group 12
Topological space, compact 13
Topology product 11
Topology quotient 33 212
Torus, maximal 251 255
Torus, of rank r 252
Torus, standard 252
Translation subgroup 19
TRANSPOSE 20
Trivial centre 70
Unimodular 4
Unimodular group 5
Unimodular matrix 4
Union, disjoint 21
Unipotent matrix 18
Unipotent subgroup 18
Unit sphere 144
Unitary group 27
Unitary group, projective 219
Universal property 132
Universal property of a Clifford algebra 132
Universal propertyof the quotient topology 213
Upper triangular matrix 18 171
Upper triangular strictly 81
Upper triangular subgroup 18
Vector product 68
Weyl group 260 292
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