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

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.