Manin triples associated to n-Lie bialgebras

Abstract

A bstract . 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.