Manin triples associated to $n$-Lie bialgebras

TL;DR

This paper explores the structure of Manin triples in relation to $n$-Lie bialgebras, introducing operad matrices and establishing a correspondence between doubles and Manin triples, advancing the theoretical understanding of $n$-Lie algebra structures.

Contribution

It introduces operad matrices for $n$-Lie bialgebras and establishes a correspondence between their doubles and Manin triples, providing new theoretical insights.

Findings

Introduction of operad matrices for $n$-Lie bialgebras

Definition of local cocycle $n$-Lie bialgebras

One-to-one correspondence between doubles and Manin triples

Abstract

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