Manin triples associated to $n$-Lie bialgebras

Abstract

In this paper, we study the Manin triples associated to $n$-Lie bialgebras. We develop the method of double constructions as well as operad matrices to make $n$-Lie bialgebras into Manin triples. Then, the related Manin triples lead to a natural construction of metric $n$-Lie algebras. Moreover, a one-to-one correspondence between the double of $n$-Lie bialgebras and Manin triples of $n$-Lie algebras be established