Abstract:

We compute   $\frac{1}{2}$-derivations on the extended Schrödinger-Virasoro algebras and the  original deformative  Schrödinger-Virasoro algebras.  The extended Schrödinger-Virasoro  algebras have neither nontrivial  $\frac{1}{2}$-derivations nor nontrivial transposed Poisson algebra structures. We demonstrate that the  original deformative  Schrödinger-Virasoro algebras have nontrivial  $\frac{1}{2}$-derivations, indicating that they possess  nontrivial  transposed Poisson structures.