  We classify Algebraic Ricci Solitons of three-dimensional Lorentzian Lie
groups. All algebraic Ricci solitons that we obtain are sol-solitons. In
particular, we prove that, contrary to the Riemannian case, Lorentzian Ricci
solitons need not to be algebraic Ricci solitons.
  We classify Algebraic Ricci Solitons of three-dimensional Lorentzian Lie
groups. All algebraic Ricci solitons that we obtain are solvsolitons. In
particular, we obtain new solitons on $G_{2}$, $G_{5}$, and $G_{6}$, and we
prove that, contrary to the Riemannian case, Lorentzian Ricci solitons need not
to be algebraic Ricci solitons.
