• Korean Journal of Mathematics
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• v.32 no.3
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• pp.425-438
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• 2024

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.