Killing Vectors and Bochner-Type Theorems in Pseudo-Riemannian Hom-Lie Algebras

In this paper, we study pseudo-Riemannian Hom-Lie algebras. We establish Hom-versions of the classical Bochner theorem in both the Riemannian and Lorentzian settings. Finally, we prove that the space of Killing vectors on a pseudo-Riemannian Hom-Lie algebra forms a totally geodesic Hom-Lie subalgebra.