Calviño Louzao, EstebanGarcía Río, EduardoGutiérrez Rodríguez, Ixchel DzoharaVázquez Lorenzo, Ramón2025-07-072025-07-072025-07-07Calviño-Louzao, E., García-Río, E., Gutiérrez-Rodríguez, I. et al. Conformally Einstein Lorentzian Lie Groups: The Non-solvable Case. J Nonlinear Sci 35, 86 (2025). https://doi.org/10.1007/s00332-025-10183-20938-8974https://hdl.handle.net/10347/42405We describe all left-invariant Bach-flat Lorentz metrics on non-solvable four-dimensional Lie groups, showing that they are conformally Einstein if and only if they are locally conformally flat. As a consequence we show the existence of strictly Bach-flat left-invariant metrics on SU(2)xR whose restriction to SU(2) may be positive definite, Lorentzian or degenerate.eng© The Author(s) 2025. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.http://creativecommons.org/licenses/by/4.0/Conformally EinsteinBach tensorC-spaceLie groupjournal article10.1007/s00332-025-10183-21432-1467open access