Existence of triangular Lie bialgebra structures II

TL;DR

This paper characterizes finite-dimensional Lie algebras over fields of characteristic zero that can admit non-trivial triangular Lie bialgebra structures, expanding understanding of their algebraic properties.

Contribution

It provides a complete characterization of Lie algebras with non-trivial triangular Lie bialgebra structures over arbitrary fields of characteristic zero.

Findings

Identifies conditions under which Lie algebras admit such structures

Classifies all finite-dimensional Lie algebras with these properties

Extends previous results to arbitrary fields of characteristic zero

Abstract

We characterize finite-dimensional Lie algebras over an arbitrary field of characteristic zero which admit a non-trivial (quasi-) triangular Lie bialgebra structure.