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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