3-Bihom-ρ-Lie Algebras, 3-Pre-Bihom-ρ-Lie Algebras

摘要

The purpose is to introduce the notions of 3-Bihom-ρ-Lie algebras and 3-preBihom-ρ-Lie algebras.The authors describe their constructions and express the related lemmas and theorems.Also,they define the 3-Bihom-ρ-Leibniz algebras and show that a3-Bihom-ρ-Lie algebra is a 3-Bihom-ρ-Leibniz algebra with theρ-Bihom-skew symmetry property.Moreover,a combination of a 3-Bihom-ρ-Lie algebra bracket and a Rota-Baxer operator gives a 3-pre-Bihom-ρ-Lie algebra structure.