On universal α-central extensions of Hom-preLie algebras

We introduce the notion of Hom-co-represention and low-dimensional chain complex. We study universal central extensions of Hom-preLie algebras and generlize some classical results. As the same time, we introduce $\alpha$-central extensions, universal $\alpha$-central extensions and $\alpha$-perfect Hom-preLie algebras. We construct universal ($\alpha$)-central extensions of Hom-preLie algebras.