Transposed Poisson structures on the extended Schr\"odinger-Virasoro and the original deformative Schr\"odinger-Virasoro algebras

TL;DR

This paper investigates transposed Poisson structures on specific Schr"odinger-Virasoro algebras, revealing the presence of nontrivial structures in the deformative case but not in the extended version.

Contribution

It computes 1/2-derivations on these algebras and characterizes their transposed Poisson structures, highlighting differences between extended and deformative types.

Findings

Extended Schr"odinger-Virasoro algebras lack nontrivial 1/2-derivations and transposed Poisson structures.

Deformative Schr"odinger-Virasoro algebras have nontrivial 1/2-derivations and transposed Poisson structures.

Abstract

We compute 1/2-derivations on the extended Schr\"odinger-Virasoro algebras and the original deformative Schr\"odinger-Virasoro algebras. The extended Schr\"odinger-Virasoro algebras have neither nontrivial 1/2-derivations nor nontrivial transposed Poisson algebra structures. We demonstrate that the original deformative Schr\"odinger-Virasoro algebras have nontrivial 1/2-derivations, indicating that they possess nontrivial transposed Poisson structures.