Inserted: 3 jun 2020
Last Updated: 3 jun 2020
Journal: Annales Mathematiques Blaise Pascal
Averages are invariants defined on the $\ell^1$ cohomology of Lie groups. We prove that they vanish for abelian and Heisenberg groups. This result completes work by other authors and allows to show that the $\ell^1$ cohomology vanishes in these cases.