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| Baker A. — Matrix Groups: An Introduction to Lie Group Theory |
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| Предметный указатель |
 -decomposition 226
 -manifold 182
 -Lie algebra 67
-line in  217
-matrix group 15
-nonn 7 33 111
-projective space 217
 -grading 136
Abelian Lie algebra 69
Action, adjoint 49 75 86 188
Action, continuous 37
Action, group 37
Action, linear 38
Action, smooth 208
Adjoint action 49 75 86 188
Adjoint representation 75
Affine geometry 19
Affine group 18
Affine transformation 19
Algebra 99
Algebra, automorphism 101
Algebra, automorphisms, group of 122
Algebra, Clifford 130
Algebra, commutative 100
Algebra, division 100
Algebra, finite dimensional 4 99
Algebra, group 100
Algebra, homomorphism 101
Algebra, isomorphism 101
Algebra, Lie 59 67
Algebra, Lorentz Clifford 177
Algebra, norm 111
Algebra, normed 111
Algebra, real Clifford 130
Algebra, semi-simple 106
Algebra, simple 104
Alternating group 153
Anti-homomorphism of skew rings 120
Atlas 182
Automorphism, canonical 134
Automorphism, inner 124
Automorphism, of algebras 101
Automorphism, outer 124
Basis, dual 290
Binary expansion 131
Borel subgroup 18
Bracket, Lie 68
Bruhat decomposition 226
Canonical automorphism 134
Canonical commutation relation 205
Cartan decomposition 280
Cartan matrix 297
Cauchy sequence 10
Central idempotent 104
Central subfield 102
Centre 69 151
Centre of a Lie algebra 69
Centre, trivial 70
Centreless 70
Character, irreducible, complex 108
Characteristic polynomial 51
Chart 182
Circle group 251
Clifford algebra 130
Clifford algebra, Lorentz 177
Clifford algebra, real 130
Clifford algebra, universal property of 132
Clifford group 139
Clifford group, finite 155
Clopen 17
Closed subset 8
Closure 41
Commutative algebra 100
Commutator 68
Commutator, subalgebra 69
Commute 68
Compact 12 13
Compact topological space 13
Complement, orthogonal 274
complete 10
Complete norm 10
Complex dimension 72
Complex matrix group 29
Complex structure 209
Complexification 92
Component path 241
conjugate 258
Conjugate, hermitian 27
Conjugate, quaternionic 120
Conjugation, map 187
Conjugation, quaternionic 120
Connected 235
Connected, by a path 241
Connected, Dynkin diagram 298
Connected, path 235
Continuous group action 37
Continuous homomorphism 31
Continuous isomorphism of matrix groups 32
Continuous map 7
Coordinate function 8
Coroot 300
Coroot, simple 300
Covering, finite 274
Cross product 68
Curve, differentiable 55 57 183
Curve, smooth 183
Derivation property 77
Derivative 74
Derived subalgebra 69
Determinant, reduced 116
Diagonalisable 51
Diffeomorphism 181
Differentiable 183
Differentiable curve 55 57 183
Differentiable homomorphism 74
Differentiable map 73
Differential geometry 181
DIMENSION 72
Dimension, complex 72
Direct isometry 22
Direct product 19 71 101
Disc, open 7
Disjoint union 21
Division algebra 100
Dual basis 290
Dual linear 289
Dual root, system 301
Dynkin diagram 298
Dynkin diagram, connected 298
Dynkin diagram, irreducible 298
Elementary 2-group 154
Euler characteristic 256
Exponential function 47
Extraspecial 2-group 154
Field, skew 100
Finite Clifford group 155
Finite covering 274
Finite dimensional algebra 4 99
Flow line 63
Form, skew symmetric 229
Form, symplectic 26 229
Function, coordinate 8
Function, exponential 47
Function, logarithm 48
Fundamental root 292
Future pointing light cone 158
Gaussian elimination 226
General linear group 5 35
Generalised permutation matrix 132
Generated by a subset 144
| Generator 254
Generator, topological 254
Geometry, affine 19
Geometry, symplectic 26
Grassmannian 222
Group, -matrix 15
Group, action 37
Group, action, continuous 37
Group, affine 18
Group, algebra 100
Group, alternating 153
Group, circle 251
Group, Clifford 139
Group, finite Clifford 155
Group, general linear 5 35
Group, Heisenberg 203
Group, inner automorphism 124
Group, isometry 22
Group, Lie 187
Group, Lorentz 26
Group, matrix 15
Group, of algebra automorphisms 122
Group, of path components 242
Group, one-parameter 57
Group, orthogonal 20
Group, outer automorphism 124
Group, pinor 143
Group, projective, linear 125 219
Group, quasi-symplectic 233
Group, quaternionic symplectic 121
Group, smooth 208
Group, special linear 5
Group, special orthogonal 21
Group, special unitary 28
Group, spinor 144
Group, symmetric 153
Group, symplectic 27
Group, topological 12
Group, unimodular 5
Group, unitary 27
Group, Weyl 260 292
Hamiltonian 118
Hausdorff space 14
Heisenberg algebra 205
Heisenberg group 203
Heisenberg — Lie algebra 205
Hermitian conjugate 27
Hermitian skew 83
Homeomorphism 14
Homogeneous polynomial 38
Homogeneous space 214
Homomorphism, algebra 101
Homomorphism, continuous 31
Homomorphism, differentiable 74
Homomorphism, Lie 74
Homomorphism, of algebras 101
Homomorphism, of Lie algebras 70
Homomorphism, property 57
Hyperplane 23
Hyperplane, reflection 23 291
Ideal, Lie 69
Idempotent 104
Idempotent, central 104
Idempotent, indecomposable 105
Idempotent, orthogonal 104
Indecomposable idempotent 105
Indirect isometry 22
Inner automorphism 124
Inner automorphism, group 124
Inner product 227
Inner product, invariant 269
Inner product, Lorentz 157
Inner product, non-degenerate 227
Inner product, positive definite 228
Inner product, real 86
Inner products, related 227
Invariant 87
Invariant, inner product 269
Irreducible complex character 108
Irreducible Dynkin diagram 298
Isometry 21 158
Isometry, direct 22
Isometry, group 22
Isometry, indirect 22
Isometry, linear 21
Isomorphism of algebras 101
Isomorphism of Lie algebras 70 86
Isomorphism, continuous, of matrix groups 32
Jacobi identity 68
Jacobian matrix 184
Jordan block matrix 52
Jordan form 51 53 79
Kronecker symbol 20
Lefschetz fixed point theorem 256
Left multiplication map 187
Left regular representation 103
Lie algebra 59 67
Lie algebra, abelian 69
Lie algebra, Heisenberg 205
Lie algebra, homomorphism 70
Lie algebra, isomorphism 70 86
Lie algebra, quotient 70
Lie algebra, simple 70
Lie bracket 67 68
Lie group 187
Lie group, semi-simple 276
Lie group, simple 274
Lie homomorphism 74
Lie ideal 69
Lie ideal, proper 69
Lie subalgebra 69
Lie subgroup 187
Light cone 158
Light cone, future pointing 158
Light cone, negative 158
Light cone, past pointing 158
Light cone, positive 158
Linear action 38
Linear dual 289
Linear isometry 21
Local trivialisation 214
Locally path connected 235
Logarithm function 48
Lorentz group 26
Lorentz inner product 157
Lorentz — Clifford algebra 177
Lower triangular matrix 171
Manifold 182
Manifold, smooth 181
Map, conjugation 187
Map, differentiate 73
Map, left multiplication 187
Map, right multiplication 187
Map, smooth 181 182
Matrix, Cartan 297
Matrix, complex 29
Matrix, diagonalisable 51
Matrix, generalised permutation 132
Matrix, group 15
Matrix, Jacobian 184
Matrix, Jordan block 52
Matrix, lower triangular 171
Matrix, orthogonal 20
Matrix, permutation 153
Matrix, subgroup 15 16
Matrix, unimodular 4
Matrix, unipotent 18
Matrix, upper triangular 18 171
Maximal 255
Maximal torus 251
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