Graded post-Lie algebra structures and homogeneous Rota-Baxter operators on the Schrödinger-Virasoro algebra (Q2046926)

The Schrödinger-Virasoro Lie algebra \(\mathcal{SV}(\varepsilon)\) is said to be twisted if \(\varepsilon=0\), and to be original if \(\varepsilon=\frac{1}{2}\). The authors complete classify the graded post-Lie algebra structures on \(\mathcal{SV}(0)\), while the corresponding results for \(\mathcal{SV}(\frac{1}{2})\) can be obtained similarly and so are omitted. As an application, the authors characterize the forms of homogeneous Rota-Baxter operators of weight \(1\) on \(\mathcal{SV}(0)\).