Every smooth p-adic Lie group admits a compatible analytic structure

Helge Glöckner 1
  • 1 TU Darmstadt, FB Mathematik AG 5, Schlossgartenstr. 7, 64289 Darmstadt, Germany.


We show that every finite-dimensional p-adic Lie group of class Ck (where k ∈ ℕ ∪ {∞}) admits a Ck-compatible analytic Lie group structure. We also construct an exponential map for every k + 1 times strictly differentiable (SCk+1) ultrametric p-adic Banach-Lie group, which is an SC1-diffeomorphism and admits Taylor expansions of all finite orders ≤ k.

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