Two constructions of grading-restricted vertex (super)algebras

TL;DR

This paper presents two novel methods for constructing grading-restricted vertex (super)algebras, including a new approach for a known class and a generalization of the moonshine module, expanding the toolkit for algebraic structures in conformal field theory.

Contribution

It introduces a new construction method for certain grading-restricted vertex (super)algebras and generalizes the author's previous work on the moonshine module, using new definitions and properties of intertwining operators.

Findings

New construction method for a class of grading-restricted vertex (super)algebras.

Generalization of the moonshine module vertex operator algebra.

Utilization of new definitions of vertex operators and intertwining properties.

Abstract

We give two constructions of grading-restricted vertex (super)algebras. We first give a new construction of a class of grading-restricted vertex (super)algebras originally obtained by Meurman and Primc using a different method. This construction is based on a new definition of vertex operators and a new method. Our second construction is a generalization of the author's construction of the moonshine module vertex operator algebra and a related vertex operator superalgebra. This construction needs properties of intertwining operators formulated and proved by the author.