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

Bing Sun; Liangyun Chen; Yan Cao; Bing Sun; Liangyun Chen; Yan Cao

doi:10.3934/era.2021004

Electronic Research Archive

2021, Volume 29, Issue 4: 2619-2636. doi: 10.3934/era.2021004

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

Bing Sun ^{1
,},
Liangyun Chen ^{2
,
,},
Yan Cao ^{3
,}

1.
School of Mathematics, Changchun Normal University, Changchun 130032, China
2.
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
3.
Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China

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.
- Hom-preLie algebra,
- Hom-action,
- universal central extension,
- universal α-central extension
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

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Abstract

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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