Abstract
The aim of this paper is to extend the notion of Leibniz bialgebra (and Lie bialgebra) to [Formula: see text]-Leibniz bialgebra (and [Formula: see text]-Lie bialgebra) by use of the cohomology complex of [Formula: see text]-Leibniz algebras. Some theorems about Leibniz bialgebras are extended and proved in the case of [Formula: see text]-Leibniz bialgebras ([Formula: see text]-Lie bialgebras). Moreover, a new theorem on the correspondence between [Formula: see text]-Leibniz bialgebra and its associated Leibniz bialgebra is proved. Finally, some examples are discussed in detail.
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