simple Lie algebra $sl(2,Q_p)$ over $p$-adic field

Question

If $L$ is the simple Lie algebra $sl(2,Q_p)$, where $Q_p$ is the $p$-adic field. Can we find an open pro-$p$ subgroup of $Aut(L)$ such that $L(U)\otimes Q_p$ is isomorphic to $L$, for some uniform subgroup of $P$?