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