Quantization of Schr\"odinger-Virasoro Lie algebra

TL;DR

This paper applies Drinfel'd twist quantization to the Schr"odinger-Virasoro Lie algebra, constructing new Hopf algebra structures and expanding the class of noncommutative, noncocommutative Hopf algebras.

Contribution

It introduces two new Drinfel'd twists for quantizing the Schr"odinger-Virasoro Lie algebra, extending existing examples of such Hopf algebras.

Findings

Constructed two distinct Hopf algebra structures

Extended the class of known noncommutative Hopf algebras

Demonstrated the quantization of the Schr"odinger-Virasoro algebra

Abstract

In this paper, we use the general quantization method by Drinfel'd twists to quantize the Schr\"odinger-Virasoro Lie algebra whose Lie bialgebra structures were recently discovered by Han-Li-Su. We give two different kinds of Drinfel'd twists, which are then used to construct the corresponding Hopf algebraic structrues. Our results extend the class of examples of noncommutative and noncocommutative Hopf algebras.