John Stillwell - Naive Lie Theory.pdf - Index of

210 Index
Lorentz, 113
matrix, vii, 3
multiplicative notation, 24
nonabelian, 27
nonmatrix, 72, 202
of generalized rotations, 22
of linear transformations, 3
of rotations of R 3 ,16
of unit quaternions, 10
orthogonal, 48, 51
path-connected, 52, 56, 118
polyhedral, 34
quotient, 23, 28
simple, 31
simply connected, 201
special linear, 93, 108, 116
special orthogonal, 3, 48, 51
special unitary, 32, 48
sporadic, 203
symplectic, 48, 57
theory, 23
unitary, 48, 55
Hadamard, Jacques, 100
Hall, Brian, 149
Halmos, Paul, ix
Hamilton, Sir William Rowan, 10
and quaternion exponential,
91, 159
definition of C,20
Hausdorff, Felix, 153
Hermite, Charles, 55
Hilbert, David, 159
fifth problem, 159
homeomorphism, 107, 168
local, 179
preserves closure, 168
homomorphism
det, 31, 107
induced, 121, 191
Lie, 191
of groups, 23, 28
of Lie algebras, 120, 186, 191
of Lie groups, 183, 186, 191
of S 3 × S 3 onto SO(4), 42
of S 3 onto SO(3),23
of simply connected groups, 201
onto quotient group, 28
theorem for groups, 30, 107
trace, 193
homotopy see deformation 177
Hopf fibration, 26
hyperplane, 36
ideal, 116
as image of normal subgroup, 117,
118
as kernel, 120
definition, 117
in gl(n,C), 122
in ring theory, 117
in so(4), 123
in u(n), 124
origin of word, 117
identity
complex two-square, 11
eight-square, 22
four-square, 11
Jacobi, 13
two-square, 6
identity component, 54, 174
is a subgroup, 54
is normal subgroup, 175
of O(3), 189
infinitesimal elements, 45, 113
inner product, 83
and angle, 49
and distance, 49, 54
and orthogonality, 49
Hermitian, 55
preservation criterion, 55
on C n ,54
on H n ,57
on R 3 ,13
on R n ,48
definition, 49
intermediate value theorem, 46
inverse function theorem, viii