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We prove some $L^p$-Liouville theorems for hypoelliptic second order PartialDifferential Operators left translation invariant with respect to a Lie groupcomposition law in $\mathbb{R}^n$. Results for both solutions and subsolutionsare given.

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