Involutive and oriented dendriform algebras

Dendriform algebras are certain splitting of associative and arise naturally from Rota-Baxter operators, shuffle planar binary trees. In this paper, we first consider involutive dendriform algebras, their cohomology homotopy analogs. The an algebra splits the Hochschild algebra. next, introduce a more general notion oriented algebras. We develop theory for that closely related to extensions governs simultaneous deformations structures orientation.