مشخصات پژوهش

Our purpose in this article is to define the compatible Poisson - Nijenhuis structure of the Co-adjoint orbit of a Lie groupoid. That is, we consider a PoissonNijenhuis structure for a Lie groupoid and by using it, we calculate the Poisson-Nijenhuis structure corresponding to its Co-adjoint Lie groupoid. In the following, we want to state the definitions and theorems for Λ-n structures on the Lie algebroid corresonding to a Lie groupoid. Also,we show that Λ-n structures can be used to find compatible solutions of the classical Yang-Baxter equation.