Abstract
In this paper, we study the Manin triples associated to [Formula: see text]-Lie bialgebras. We introduce the concept of operad matrices for [Formula: see text]-Lie bialgebras. In particular, by studying a special case of operad matrices, it leads to the notion of local cocycle [Formula: see text]-Lie bialgebras. Furthermore, we establish a one-to-one correspondence between the double of [Formula: see text]-Lie bialgebras and Manin triples of [Formula: see text]-Lie algebras.
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