Representations and formal deformations of Leibniz H-pseudoalgebras

In this paper, we first give some constructions of right (resp. left) Leibniz H-pseudoalgebras and explore the characterization of symmetric Leibniz H-pseudoalgebras. Furthermore, we introduce the notion of relative Rota-Baxter H-operator and show that a right (resp. left) Leibniz H-pseudoalgebra together with a relative Rota-Baxter H-operator gives rise to a representation of related right (resp. left) Leibniz H-pseudoalgebra. Finally, we describe the central extension and the formal deformation in terms of the corresponding second cohomology group.