Leibniz H-pseudoalgebras

We define a Leibniz H-pseudoalgebra over a cocommutative Hopf algebra H, and a tensor product of Leibniz H-pseudoalgebras, and prove that every Leibniz H-pseudoalgebra of free rank one over H is a Lie H-pseudoalgebra. To characterize simple Leibniz H-pseudoalgebras, we define the Leibniz cohomology of Leibniz H-pseudoalgebras and determine some simple Leibniz H-pseudoalgebras by calculating Leibniz cohomological groups of finite simple Lie H-pseudoalgebras defined in [2].