On the universal central extension of superelliptic affine Lie algebras

TL;DR

This paper explicitly describes the universal central extension of a specific infinite-dimensional Lie algebra constructed from a simple Lie algebra and a superelliptic curve, using generators and relations.

Contribution

It provides an explicit presentation of the universal central extension for superelliptic affine Lie algebras, which was previously not well-understood.

Findings

Explicit generators and relations for the extension are derived.

The structure of the universal central extension is clarified in the superelliptic case.

Abstract

The goal of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, $\mathfrak{g} \otimes \mathbb{C}[t,t^{-1},u]$ with finite dimensional simple Lie algebra $\mathfrak{g}$ and $u^m=p(t)$.