The Schr\"{o}dinger-Virasoro type Lie bialgebra: a twisted case

TL;DR

This paper classifies Lie bialgebra structures on a twisted Schr"{o}dinger-Virasoro algebra, revealing all are triangular coboundary and uncovering additional hidden inner derivations unique to this twisted case.

Contribution

It demonstrates that all Lie bialgebra structures on the twisted algebra are triangular coboundary and introduces a method to identify hidden inner derivations.

Findings

All structures are triangular coboundary.

More hidden inner derivations exist in the twisted case.

Developed a new method to find inner derivations.

Abstract

In this paper we investigate Lie bialgebra structures on a twisted Schr\"{o}dinger-Virasoro type algebra $\LL$. All Lie bialgebra structures on $\LL$ are triangular coboundary, which is different from the relative result on the original Schr\"{o}dinger-Virasoro type Lie algebra. In particular, we find for this Lie algebra that there are more hidden inner derivations from itself to $\LL\otimes\LL$ and we develop one method to search them.