On the Universal $$\alpha $$α-Central Extension of the Semi-direct Product of Hom-Leibniz Algebras

@article{Casas2013OnTU,
  title={On the Universal \$\$\alpha \$\$$\alpha$-Central Extension of the Semi-direct Product of Hom-Leibniz Algebras},
  author={Jos{\'e} Manuel Casas and N. Pacheco Rego},
  journal={Bulletin of the Malaysian Mathematical Sciences Society},
  year={2013},
  volume={39},
  pages={1579-1602}
}
  • J. Casas, N. P. Rego
  • Published 20 September 2013
  • Mathematics
  • Bulletin of the Malaysian Mathematical Sciences Society
We introduce Hom-actions, semidirect product, and establish the equivalence between split extensions and the semi-direct product extension of Hom-Leibniz algebras. We analyze the functorial properties of the universal ($$\alpha $$α)-central extensions of ($$\alpha $$α)-perfect Hom-Leibniz algebras. We establish under what conditions an automorphism or a derivation can be lifted in an $$\alpha $$α-cover and we analyze the universal $$\alpha $$α-central extension of the semi-direct product of two… 
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On the universal $ \alpha $-central extensions of the semi-direct product of Hom-preLie algebras
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…

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