Abstract
The purpose of this study is to introduce the (almost) cosymplectic Hom–Lie algebras and to show that these Hom–Lie algebras and symplectic Hom–Lie algebras are related to each other. We also describe the notion of the almost coKähler structures on Hom–Lie algebras and show that they are related to almost Kähler structures. The properties of the curvature tensor of such structures are presented in this study. \(\eta \)-Einstein almost coKähler Hom–Lie algebras are described as well. We give the notions of Hom-\(\eta \)-parallel and Hom-cyclic parallel. Finally, some conditions for an almost Kähler structure induced by an almost coKähler Hom–Lie algebra to be totally geodesic are given.
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Peyghan, E., Nourmohammadifar, L., Gezer, A. et al. CoKähler and Cosymplectic Hom–Lie Algebras. Mediterr. J. Math. 20, 90 (2023). https://doi.org/10.1007/s00009-023-02282-9
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DOI: https://doi.org/10.1007/s00009-023-02282-9