How far are p-adic Lie groups from algebraic groups?

Yves Benoist (1) , Jean-François Quint (2)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 IMB - Institut de Mathématiques de Bordeaux

We show that, in a weakly regular $p$-adic Lie group $G$, the subgroup $G_u$ spanned by the one-parameter subgroups of $G$ admits a Levi decomposition. As a consequence, there exists a regular open subgroup of $G$ which contains $G_u$.

Mots clés: p-adic Lie group; algebraic group; unipotent subgroup; Levi decomposition; central extension

Domaines: Théorie des groupes [math.GR]

Yves Benoist, Jean-François Quint. How far are p-adic Lie groups from algebraic groups?. 2021. ⟨hal-03120382⟩