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We describe the universal central extension of the three point currentalgebra $\mathfrak{sl}(2,\mathcal R)$ where $\mathcal R=\mathbbC[t,t^{-1},u\,|\,u^2=t^2+4t ]$ and construct realizations of it in terms ofsums of partial differential operators.

Realizations of the three point algebra $\mathfrak{sl}(2, \mathcal R) \oplus\left(\Omega_{\mathcal R}/d{\mathcal R}\right)$