Some finite properties for vertex operator superalgebras

TL;DR

This paper investigates properties of vertex operator superalgebras, focusing on their rationality and subalgebra structures, and establishes that the rationality of the even part implies the rationality of the entire superalgebra.

Contribution

It determines the subalgebras generated by specific weight spaces and proves that the rationality of the even part ensures the superalgebra's rationality.

Findings

Subalgebras generated by weight 1/2 and 1 are characterized.

Rationality of the even part implies the rationality of the whole superalgebra.

Various results on rational vertex operator superalgebras are obtained.

Abstract

Vertex operator superalgebras are studied and various results on rational Vertex operator superalgebras are obtained. In particular, the vertex operator super subalgebras generated by the weight 1/2 and weight 1 subspaces are determined. It is also established that if the even part $V_{\bar 0}$ of a vertex operator superalgebra $V$ is rational, so is $V.$