University of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05003220221201Para-Kähler hom-Lie algebras of dimension 2119138196010.22098/jfga.2022.11916.1079ENEsmaeil PeyghanDepartment of Mathematics, Faculty of Science, Arak university, Arak, IranLeila NourmohammadifarDepartment of Mathematics, Faculty of Science, Arak University
Arak, 38156-8-8349, Iran.Journal Article20221212In [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.https://jfga.uma.ac.ir/article_1960_c36f1d44ba66eb9cdf7397e967864f41.pdf