### Electronic Research Archive

2021, Issue 4: 2619-2636. doi: 10.3934/era.2021004

# On the universal $\alpha$-central extensions of the semi-direct product of Hom-preLie algebras

• Received: 01 October 2020 Revised: 01 November 2020 Published: 01 September 2021
• Primary: 17A30; Secondary: 16E40

• We study Hom-actions, semidirect product and describe the relation between semi-direct product extensions and split extensions of Hom-preLie algebras. We obtain the functorial properties of the universal $\alpha$-central extensions of $\alpha$-perfect Hom-preLie algebras. We give that a derivation or an automorphism can be lifted in an $\alpha$-cover with certain constraints. We provide some necessary and sufficient conditions about the universal $\alpha$-central extension of the semi-direct product of two $\alpha$-perfect Hom-preLie algebras.

Citation: Bing Sun, Liangyun Chen, Yan Cao. On the universal $\alpha$-central extensions of the semi-direct product of Hom-preLie algebras[J]. Electronic Research Archive, 2021, 29(4): 2619-2636. doi: 10.3934/era.2021004

### Related Papers:

• We study Hom-actions, semidirect product and describe the relation between semi-direct product extensions and split extensions of Hom-preLie algebras. We obtain the functorial properties of the universal $\alpha$-central extensions of $\alpha$-perfect Hom-preLie algebras. We give that a derivation or an automorphism can be lifted in an $\alpha$-cover with certain constraints. We provide some necessary and sufficient conditions about the universal $\alpha$-central extension of the semi-direct product of two $\alpha$-perfect Hom-preLie algebras.

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