John Stillwell - Naive Lie Theory.pdf - Index of

212 Index
knew SO(4) anomaly, 47
Transformationsgruppen,47
Lie-type finite groups, 203
lifting, 179
a deformation, 180
a Lie algebra homomorphism, 197
a path, 179
limit point, 4, 162
linear transformations, 2
group of, 3
of H,39
of H n ,57
orthogonal, 3
preserving inner product, 48, 49
on C n ,55
preserving length, 49, 161
preserving orientation, 48, 50
locus, 173
log see logarithm function 139
logarithm function
inverse to exp, 140
multiplicative property,
141, 146
produces tangents, 139
M n (C), 108
M n (H), 111
M n (R), 93
manifold, 3
Riemannian, 92
matrix
absolute value, 84
submultiplicative property, 84
block multiplication, 41
criterion for rotation, 50
dilation, 51
exponential function, 84
definition, 86
groups, vii
inverse, 6
Lie algebra, 105
Lie group see matrix Lie groups 81
orthogonal, 32, 51, 97
product properties, 8
quaternion, 57, 112
representation of H, 7
discovered by Cayley, 10
representation of C, 5
representation of linear functions,
27, 87
sequence, 161
skew-Hermitian, 96, 99
skew-symmetric, 93, 96, 99
special orthogonal, 50
transpose, 10, 58
unitary, 32
upper triangular, 100
matrix group, 3
abelian, 41
closed, 143, 164
Lie see matrix Lie groups 81
quotient, 72
smoothness of, 3
matrix Lie groups, 4, 81, 113
and topology, 160
are closed, 164
are smooth manifolds, 147
as subgroups of GL(n,C),
160, 165
closed under limits, 4, 88,
139, 147
defined by von Neumann, 158
definition, 4, 143, 166
include finite groups, 114
spawn finite groups, 203
matrix logarithm see logarithm function
139
maximal abelian subgroup, 66
maximal torus, 48, 60
in GL(n,C), 111
in SL(n,C), 111
in SO(2m),64
in SO(2m + 1), 64, 65
in SO(3),60
in Sp(n), 66
in SU(n),66