On the Universal Central Extension of Hyperelliptic Current Algebras

Abstract

Let $p(t)\in\mathbb C[t]$ be a polynomial with distinct roots and nonzero constant term. We describe, using Faá de Bruno's formula and Bell polynomials, the universal central extension in terms of generators and relations for the hyperelliptic current Lie algebras $\mathfrak g\otimes R$ whose coordinate ring is of the form $R=\mathbb C[t,t^{-1},u\,|\, u^2=p(t)]$.

Sign change, name change in the last theorem