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Baker A. — Matrix Groups: An Introduction to Lie Group Theory
Baker A. — Matrix Groups: An Introduction to Lie Group Theory



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Название: Matrix Groups: An Introduction to Lie Group Theory

Автор: Baker A.

Аннотация:

Throughout the text, the emphasis is on providing an approach that is accessible to readers equipped with a standard undergraduate toolkit of algebra and analysis. Although the formal prerequisites are kept as low level as possible, the subject matter is sophisticated and contains many of the key themes of the fully developed theory, preparing students for a more standard and abstract course in Lie theory and differential geometry.


Язык: en

Рубрика: Математика/Алгебра/Теория представлений/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 343

Добавлена в каталог: 19.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$LPU$-decomposition      226
$n$-manifold      182
$\Bbbk$-Lie algebra      67
$\Bbbk$-line in $\Bbbk^{n+1}$      217
$\Bbbk$-matrix group      15
$\Bbbk$-nonn      7 33 111
$\Bbbk$-projective space      217
$\pm$-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, $\Bbbk$-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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