Index
Abelian Lie algebra 29
abelian Lie group 20
action 24, 66
transitive 66
Ad-invariance 33, 61
AdG'K
- invariance 78
adjoint orbit 96
adjoint representation
of a Lie group 28
of a Lie algebra 28, 41
almost complex structure 105
automorphism 14, 28
Bianchi identity, first 57
second 57
bi-invariant metric 60
Borel subgroup 111
subalgebra 111
bracket (of vector fields) 7
Campbell-Baker-Hausdorff formula
20
Cartan subalgebra 41
integer 43
Casimir operator 115
center of a Lie group 29
of a Lie algebra 29
centralizer 38, 97
chart 2
classical Lie algebras 40
Lie groups 10
classification of compact and
connected Lie groups 39
classification of irreducible symmetric
spaces 93
Clifford algebra 40
closed subgroup 10
commutative Lie algebra 20
complex structure 105
complexification 30
connection 53
constant (sectional) curvature 58
coset manifold 66
covariant derivative 55
curvature, sectional 57
scalar 59
functional 114
Ricci 58
curvature operator 57
tensor 56
curve 5, 54
Derivation 6
diffeomorphism 4
differential 5
duality of symmetric spaces 92
Dynkin diagram 40, 45
painted 99
Einstein manifold 64, 113
endomorphism 14
equivalent representations 25
exceptional Lie groups 40
exponential map 16, 56
Flag manifold 70, 97
flat 58
flow (local) 7
G-equivariant map 26
139
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