Handout: Almost inner derivations of Lie algebras by Aaron Berman
Denition 0.1.
morphism
Let G be a group and let
Φ : Γ1 → Γ2
which carries
that is conjugate in G to
this case,
Γ1
and
Γ2
γ,
Γ1 , Γ2 ⊂ G
every γ ∈ Γ1 to
is called an
be subgroups. An autoan element
Φ(γ)
of
almost inner automorphism.
Γ2
In
are called almost conjugated. The set of all almost inner
automorphism is denoted by AIA(G).
Denition 0.2.
A derivation
φ of a Lie algebra g is called an almost inner
x ∈ g φ(x) ∈ [X, g]. The set of all almost inner derivations
AID(g)
derivation if for all
is denoted by
1