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.

中文翻译：

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李群的几何表示及其Dehn函数

我们研究了连通李群的Dehn函数。我们证明，根据权重的几何及其李代数的2-同调性，该函数始终是指数或多项式有界的。我们的工作也针对本地领域的代数群，它使用并扩展了Abels的分级李代数的多重汞合金理论，以便为这些群提供可行的表述。