The three point gauge algebra $\mathcal{V}⋉\mathfrak{s}\mathfrak{l}(2,\mathcal{R})\oplus \left({\mathrm{\Omega }}_{\mathcal{R}}\mathrm{/}d\mathcal{R}\right)$ and an action on a Fock space

The three point current algebra $\mathfrak{s}\mathfrak{l}(2,\mathcal{R})$ where $\mathcal R=\mathbb C[t,t^{-1},u,|,u^2=t^2+4t ]$ and three-point Virasoro algebra both act on a previously constructed Fock space. In this paper we prove that the semi-direct product, i.e. the gauge algebra acts on the Fock space as well.