Lie bialgebra structures on extended Schrodinger-Virasoro Lie algebra

TL;DR

This paper classifies Lie bialgebra structures on the extended Schrödinger-Virasoro Lie algebra, showing all are triangular coboundary and that the first cohomology group is trivial, contributing to the understanding of its algebraic properties.

Contribution

It provides a complete classification of Lie bialgebra structures on the extended Schrödinger-Virasoro Lie algebra, revealing their triangular coboundary nature and trivial first cohomology.

Findings

All Lie bialgebra structures are triangular coboundary.

The first cohomology group is trivial.

Provides a foundation for further algebraic studies of this Lie algebra.

Abstract

In this paper, Lie bialgebra structures on the extended Schrodinger-Virasoro Lie algebra are classified. It is obtained that all the Lie bialgebra structures on L are triangular coboundary. As a by-product, it is derived that the first cohomology group is trivial.