The construction of Hom-Leibniz H-pseudoalgebras

Abstract

This paper is devoted to the construction of Hom-Leibniz $H$-pseudoalgebras, which unify Hom-Lie $H$-pseudoalgebras, Leibniz $H$-pseudoalgebras and Hom-Leibniz algebras. Firstly, we give the construction theorem and obtain a class of Hom-Leibniz $H$-pseudoalgebras. We also construct Hom-Leibniz $H$-pseudoalgebras from different perspective, including Leibniz $H$-pseudoalgebras, Hom-Leibniz (resp. Hom-Lie, Hom-associative) $H$-pseudoalgebras and their representations, Hom-Leibniz (resp. Hom-associative) algebras. Then we give some properties of the representations of Hom-Leibniz $H$-pseudoalgebras. Finally, the annihilation algebras of Hom-Leibniz $H$-pseudoalgebras are investigated.