Transposed Poisson structures on the extended Schrödinger-Virasoro and the original deformative Schrödinger-Virasoro algebras

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.