Nijenhuis BiHom-Lie bialgebras and differential Lie bialgebras

TL;DR

This paper introduces Nijenhuis BiHom-Lie algebras, explores their equivalences with Lie bialgebras and related structures, and establishes new theoretical connections among these algebraic systems.

Contribution

It defines Nijenhuis BiHom-Lie algebras and proves their equivalence with Lie bialgebras and related structures, expanding the theoretical framework.

Findings

Established equivalence between Nijenhuis BiHom-Lie algebras and Lie bialgebras

Connected Manin triples with Nijenhuis BiHom-Lie bialgebras

Extended equivalence to differential Lie bialgebras

Abstract

In this paper, we first introduce the concept of Nijenhuis BiHom-Lie algebras. We then establish the equivalence relations between the Manin triples of Nijenhuis BiHom-Lie algebras, Nijenhuis BiHom-Lie bialgebras, and matched pairs of Nijenhuis BiHom-Lie algebras. Furthermore, we show that such an equivalence also holds for differential Lie bialgebras, together with their associated Manin triples and corresponding matched pairs.