Lie bialgebra structures on the Lie algebra $\widetilde{\frak{sl}_2(C_q[x,y])}$

TL;DR

This paper investigates the Lie bialgebra structures on a specific Lie algebra related to quantum polynomial rings, establishing that these structures are of the triangular coboundary type.

Contribution

It demonstrates that all Lie bialgebra structures on the algebra are triangular coboundary, providing a classification result for this class of algebras.

Findings

All Lie bialgebra structures are triangular coboundary.

Provides a classification of structures on the given Lie algebra.

Enhances understanding of quantum algebraic structures.

Abstract

In the present paper we shall investigate the Lie bialgebra structures on the Lie algebra $\widetilde{\frak{sl}_2(C_q[x,y])}$, which are shown to be triangular coboundary.