Constructions and representation theory of BiHom-post-Lie algebras

The main goal of this paper is to give some construction results BiHom-post-Lie algebras which are a generalization both post-Lie-algebras and Hom-post-Lie algebras. They the algebraic structures behind weighted $${\mathcal {O}}$$ -operator BiHom-Lie can be also regarded as splitting into three parts structure BiHom-Lie-algebra. Moreover we develop representation theory on vector space V. We show that there naturally an induced its sub-adjacent Lie algebra. all 2-dimensional exhibit in work important examples post-Lie