Algebraic Ricci solitons of three-dimensional Lorentzian Lie groups

We study 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 G2, G5, and G6, and we prove that, contrary to the Riemannian case, Lorentzian Ricci solitons need not be algebraic Ricci solitons.