  We study the Dehn function of connected Lie groups. We show that this
function is always exponential or polynomially bounded, according to the
geometry of weights and of the 2-cohomology of their Lie algebras. Our work,
which also addresses algebraic groups over local fields, uses and extends
Abels' theory of multiamalgams of graded Lie algebras, in order to provide
workable presentations of these groups.
