${L^p}$-Liouville Theorems for Invariant Partial Differential Operators in ${mathbb{R}^n}$

We prove some $L^p$-Liouville theorems for hypoelliptic second order Partial Differential Operators left translation invariant with respect to a Lie group composition law in $mathbb{R}^n$. Results for both solutions and subsolutions are given.