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

Ben L. Cox, Elizabeth G. Jurisich

Published 2013-03-27, updated 2015-02-22Version 3

We describe the universal central extension of 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 construct realizations of it in terms of sums of partial differential operators.