  The purpose of this paper is to explicitly describe in terms of generators
and relations the universal central extension of the infinite dimensional Lie
algebra, $\mathfrak g\otimes \mathbb C[t,t^{-1},u|u^2=(t^2-b^2)(t^2-c^2)]$,
appearing in the work of Date, Jimbo, Kashiwara and Miwa in their study of
integrable systems arising from Landau-Lifshitz differential equation.
