We determine the Lie algebras of all simply transitive groups of automorphisms of a homogeneous Siegel domain
D
D
as modifications of standard normal
j
j
-algebras. We show that the Lie algebra of all automorphisms of
D
D
is a "complete isometry algebra in standard position". This implies that
D
D
carries a riemannian metric
g
~
\tilde g
with nonpositive sectional curvature satisfying Lie
Iso
(
D
,
g
~
)
=
Lie
Aut
D
\operatorname {Iso}(D,\tilde g) = \operatorname {Lie}\; \operatorname {Aut}\, \text {D}
. We determine all Kähler metrics
f
f
on
D
D
for which the group
Aut
(
D
,
f
)
\operatorname {Aut}(D,f)
of holomorphic isometries acts transitively. We prove that in this case
Aut
(
D
,
f
)
\operatorname {Aut}(D,f)
contains a simply transitive split solvable subgroup. The results of this paper are used to prove the fundamental conjecture for homogeneous Kähler manifolds admitting a solvable transitive group of automorphisms.