Rota-Baxter Systems for BiHom-Type Algebras

The purpose of this paper is to study Rota–Baxter systems for BiHom-type algebras such as BiHom analogues of associative, dendriform, quadri algebras. It is shown that BiHom-dendriform structures of a particular kind are equivalent to Rota–Baxter systems. It is shown further that a Rota–Baxter system induces a weak BiHom-pseudotwistor which can be held responsible for the existence of a new product on the underlying BiHom-associative algebra. Moreover, we study the relationship between BiHom-quadri-algebras and Rota–Baxter systems for BiHom-dendriform algebras.