Lie Bialgebra Structures on Generalized Heisenberg-Virasoro Algebra

TL;DR

This paper classifies Lie bialgebra structures on the generalized Heisenberg-Virasoro algebra, providing explicit cohomology calculations and proving all structures on the centerless version are coboundary triangular.

Contribution

It explicitly determines the Lie bialgebra structures on the generalized Heisenberg-Virasoro algebra and its centerless form, including cohomology and structure classification.

Findings

All Lie bialgebra structures on the centerless algebra are coboundary triangular.

Explicit calculation of the first cohomology group $H^1(rak{L}, rak{L} igotimes rak{L})$.

Classification of Lie bialgebra structures on the algebra.

Abstract

In this paper, Lie bialgebra structures on generalized Heisenberg-Virasoro algebra $\mathfrak{L}$ are considered. Also, $H^1({\mathfrak{L}} ,\mathfrak{L}\bigotimes\mathfrak{L})$ is given explicitly. Moreover, it is proved that all Lie bialgebra structure on centerless generalized Heisenberg-Virasoro algebra $\bar{\mathfrak{L}}$ are coboundary triangular.