Lie 2-bialgebras

TL;DR

This paper explores the structure of Lie 2-bialgebras, focusing on coboundary cases, and introduces new examples derived from left-symmetric and symplectic Lie algebras using cohomology theory.

Contribution

It develops the cohomology theory for $L_ olinebreak_ ext{infty}$-algebras and constructs explicit examples of strict Lie 2-bialgebras from specific algebraic structures.

Findings

Established cohomology framework for Lie 2-bialgebras

Constructed examples from left-symmetric algebras

Constructed examples from symplectic Lie algebras

Abstract

In this paper, we study Lie 2-bialgebras, with special attention to coboundary ones, with the help of the cohomology theory of $L_\infty$-algebras with coefficients in $L_\infty$-modules. We construct examples of strict Lie 2-bialgebras from left-symmetric algebras and symplectic Lie algebras.