Module structure of the center of the universal central extension of a genus zero Krichever-Novikov algebra

TL;DR

This paper investigates the structure of the center in the universal central extension of genus zero Krichever-Novikov current algebras, revealing its decomposition into irreducible modules under automorphism groups.

Contribution

It provides a detailed description of how the center decomposes into irreducible modules for automorphism groups, advancing understanding of algebraic structures in Krichever-Novikov algebras.

Findings

Center decomposes as a direct sum of irreducible modules

Automorphism group actions determine module structure

Enhanced understanding of algebraic symmetries in genus zero cases

Abstract

We describe how the center of the universal central extension of the genus zero Krichever-Novikov current algebra decomposes as a direct sum of irreducible modules for automorphism group of the coordinate ring of this algebra.