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

Abstract

The purpose is to introduce the notions of 3-Bihom-ρ-Lie algebras and 3-pre-Bihom-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 a 3-Bihom-ρ-Lie algebra is a 3-Bihom-ρ-Leibniz algebra with the ρ-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.

Keywords

3-Bihom-ρ-Lie algebra / 3-Pre-Bihom-ρLie algebra / Rota-Baxer operator

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