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

Geometric presentations of Lie groups and their Dehn functions