Every affine structure on Lie algebra 𝔤 defines a
representation of 𝔤 in aff(ℝn). If 𝔤 is a nilpotent Lie algebra provided with a
complete affine structure then the corresponding representation
is nilpotent. We describe noncomplete affine
structures on the filiform Lie algebra Ln. As a consequence we give a nonnilpotent faithful linear representation of the 3-dimensional Heisenberg algebra.