A class of non-weight modules over the Schrödinger-Virasoro algebras

Abstract

We construct and classify the free $U(\mathbb{C}{L}_0\oplus \mathbb{C}{M}_0\oplus \mathbb{C}{Y}_0)$-modules of rank $1$ over the Schrödinger-Virasoro algebra $\mathfrak{sv}(s)$ for $s=0$.Moreover, we show that the class of free $U(\mathbb{C}{L}_0\oplus \mathbb{C}{M}_0)$-modules of rank $1$ over the Schrödinger-Virasoro algebra $\mathfrak{sv}(s)$ for $s=\frac{1}{2}$ is nonexistent.