On the universal central extension of superelliptic affine Lie algebras

Abstract

We describe explicitly in terms of generators and relations the universal central extension of infinite-dimensional superelliptic affine Lie algebras $\mathfrak{g}\otimes R$ with a finite-dimensional simple Lie algebra $\mathfrak{g}$ and the coordinate ring $R=\mathbb{C}[t,t^{-1},u],$ where $u^m=p(t)$ and p(t) is a polynomial with distinct roots.

Keywords:

• Affine Lie algebras
• Krichever–Novikov algebras
• superelliptic algebras
• universal central extensions

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B05

Additional information

Funding

This work was supported by CNPq (142053/2017-1).