A Generalized Vertex Operator Algebra for Heisenberg Intertwiners

TL;DR

This paper extends the Heisenberg vertex operator algebra by all its irreducible modules, constructing intertwining operators that form a generalized vertex operator algebra, with applications to lattice vertex superalgebras.

Contribution

It provides an elementary construction of intertwining operators and demonstrates their structure as a generalized vertex operator algebra.

Findings

Intertwining operators satisfy a complex parametrized algebraic structure

Construction applies to integral lattice vertex superalgebras

Shows the extended algebra's consistency and structure

Abstract

We consider the extension of the Heisenberg vertex operator algebra by all its irreducible modules. We give an elementary construction for the intertwining vertex operators and show that they satisfy a complex parametrized generalized vertex operator algebra. We illustrate some of our results with the example of integral lattice vertex operator superalgebras.