Classification of Algebraic Schouten Solitons on Lorentzian Lie Groups Associated with the Perturbed Canonical Connection and the Perturbed Kobayashi–Nomizu Connection

In this paper, we investigate the algebraic conditions of algebraic Schouten solitons on three-dimensional Lorentzian Lie groups associated with the perturbed canonical connection and the perturbed Kobayashi–Nomizu connection. Furthermore, we provide the complete classification for these algebraic Schouten solitons on three-dimensional Lorentzian Lie groups associated with the algebraic Schouten solitons. The main results indicate that G4 does not possess algebraic Schouten solitons related to the perturbed Kobayashi–Nomizu connection, G1,G2,G3,G6, and G7 possess algebraic Schouten solitons, and the result for G5 is trivial.