# Dual Lie bialgebra structures of the twisted Heisenberg-Virasoro type

## TL;DR

This paper explores the dual Lie bialgebra structures of the twisted Heisenberg-Virasoro algebra by analyzing maximal good subspaces, leading to the construction of dual structures and four new infinite-dimensional Lie algebras.

## Contribution

It introduces the dual Lie bialgebra structures for the twisted Heisenberg-Virasoro algebra and constructs four new infinite-dimensional Lie algebras.

## Key findings

- Determined the dual Lie coalgebras of the centerless twisted Heisenberg-Virasoro algebra.
- Constructed dual Lie bialgebra structures for the twisted Heisenberg-Virasoro type.
- Discovered four new infinite-dimensional Lie algebras.

## Abstract

In this paper, by studying the maximal good subspaces, we determine the dual Lie coalgebras of the centerless twisted Heisenberg-Virasoro algebra. Based on this, we construct the dual Lie bialgebras structures of the twisted Heisenberg-Virasoro type. As by-products, four new infinite dimensional Lie algebras are obtained.