  In this paper we develop an abstract setup for hamiltonian group actions as
follows: Starting with a continuous 2-cochain $\omega$ on a Lie algebra $h$
with values in an $h$-module $V$, we associate subalgebras $sp(h,\omega) \supeq
ham(h,\omega)$ of symplectic, resp., hamiltonian elements. Then $ham(h,\omega)$
has a natural central extension which in turn is contained in a larger abelian
extension of $sp(h,\omega)$. In this setting, we study linear actions of a Lie
group $G$ on $V$ which are compatible with a homomorphism $g \to
ham(h,\omega)$, i.e. abstract hamiltonian actions, corresponding central and
abelian extensions of $G$ and momentum maps $J : g \to V$.
