Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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CHARACTERIZATIONS OF BIHOM-ALTERNATIVE(-LEIBNIZ) ALGEBRAS THROUGH ASSOCIATED BIHOM-AKIVIS ALGEBRAS

  • Sylvain Attan (Departement de Mathematiques, Universite d'Abomey-Calavi)
  • Received : 2024.02.19
  • Accepted : 2024.08.29
  • Published : 2024.09.30
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Abstract

BiHom-Akivis algebras are introduced. It is shown that BiHom-Akivis algebras can be obtained either from Akivis algebras by twisting along two algebra morphisms or from a regular BiHom-algebra via the BiHom-commutator-BiHom-associator algebra. It is also proved that a BiHom-Akivis algebra associated to a regular BiHom-alternative algebra is a BiHom-Malcev algebra. Using the BiHom-Akivis algebra associated to a given regular BiHom-Leibniz algebra, a necessary and sufficient condition for BiHom-Lie admissibility of BiHom-Leibniz algebras is obtained.

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References

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