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