The three point gauge algebra mathcal Vltimes mathfrak{sl}(2, mathcal R) oplusleft(Ω_(mathcal R)/d{mathcal R}right) and an action on a Fock space

The three point current algebra $\mathfrak{sl}(2,\mathcal R)$ 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.