Schottky vertex operator cluster algebras

TL;DR

This paper introduces a new algebraic structure called vertex operator cluster algebras, extending cluster algebra concepts to higher genus Riemann surfaces using vertex operator algebra techniques.

Contribution

It defines the notion of vertex operator cluster algebra, including elements and mutation rules, and provides the simplest example of such a structure.

Findings

Defined vertex operator cluster algebra structure

Explicitly formulated cluster elements and mutations

Presented the simplest example of the structure

Abstract

Using recursion formulas for vertex operator algebra higher genus characters with formal parameters identified with local coordinates around marked points on a Riemann surface of arbitrary genus, we introduce the notion of a vertex operator cluster algebra structure. Cluster elements and mutation rules are explicitly defined, and the simplest example of a vertex operator cluster algebra is presented.