The 3-point Virasoro algebra and its action on a Fock space

TL;DR

This paper introduces a new 3-point Virasoro algebra and constructs its representation on a Fock space associated with a 3-point affine algebra, expanding the understanding of algebraic structures in mathematical physics.

Contribution

The paper defines the 3-point Virasoro algebra and constructs its explicit representation on a specialized Fock space, a novel development in the study of affine algebras.

Findings

Defined the 3-point Virasoro algebra.

Constructed a representation on a Fock space.

Extended algebraic frameworks in mathematical physics.

Abstract

We define a 3-point Virasoro algebra, and construct a representation of it on a previously defined Fock space for the 3-point affine algebra $\mathfrak{sl}(2, \mathcal R) \oplus\left( \Omega_{\mathcal R}/d{\mathcal R}\right)$.