  In this paper, we compute canonical connections and Kobayashi-Nomizu
connections and their curvature on three-dimensional Lorentzian Lie groups with
some product structure. We define algebraic Ricci solitons associated to
canonical connections and Kobayashi-Nomizu connections. We classify algebraic
Ricci solitons associated to canonical connections and Kobayashi-Nomizu
connections on three-dimensional Lorentzian Lie groups with some product
structure.
