University of Mohaghegh Ardabili Journal of Finsler Geometry and its Applications 2783-0500 3 2 2022 12 01 Para-Kähler hom-Lie algebras of dimension 2 119 138 1960 10.22098/jfga.2022.11916.1079 EN Esmaeil Peyghan Department of Mathematics, Faculty of Science, Arak university, Arak, Iran Leila Nourmohammadifar Department of Mathematics, Faculty of Science, Arak University Arak, 38156-8-8349, Iran. Journal Article 2022 12 12 In [12], authors introduced some geometric concepts such as (almost) product, para-complex, para-Hermitian and para-Kähler structures for hom-Lie algebras and they presented an example of a 4-dimensional hom-Lie algebra, which contains these concepts. In this paper, we classify two-dimensional hom-Lie algebras containing these structures. In particular, we show that there doesn't exist para-Kahler proper hom-Lie algebra of dimension 2. Almost para-Hermitian structure hom-Levi-Civita product para- Kähler hom-Lie algebra https://jfga.uma.ac.ir/article_1960_c36f1d44ba66eb9cdf7397e967864f41.pdf