Krichever-Novikov Vertex Algebras on Compact Riemann Surfaces

TL;DR

This paper introduces a generalized framework for Krichever-Novikov vertex algebras on compact Riemann surfaces, extending classical vertex algebra concepts and constructing examples related to generalized Heisenberg algebras.

Contribution

It proposes a weaker but similar notation for Krichever-Novikov vertex algebras and constructs new examples on arbitrary compact Riemann surfaces.

Findings

Defined a new notation for Krichever-Novikov vertex algebras

Constructed examples of generalized Heisenberg algebras on Riemann surfaces

Reduced to classical Heisenberg vertex algebra on Riemann spheres

Abstract

We give a notation of Krichever-Novikov vertex algebras on compact Riemann surfaces which is a bit weaker, but quite similar to vertex algebras. As example, we construct Krichever-Novikov vertex algebras of generalized Heisenberg algebras on arbitrary compact Riemann surfaces, which are reduced to be Heisenberg vertex algebra when restricted on Riemann spheres.