BiHom-pre-Lie algebras, BiHom-Leibniz algebras and Rota–Baxter operators on BiHom-Lie algebras

Abstract We contribute to the study of Rota–Baxter operators on types algebras other than associative and Lie algebras. If A is an algebra a certain type R operator , one can define new multiplication by means previous ask under what circumstances same as . Our first main result deals with such situation in case BiHom-Lie second BiHom analogue Aguiar’s theorem that shows how obtain pre-Lie from weight zero algebra. The does not work for algebras, but concept we introduce here, called left algebra, at which arrived defining version Leibniz