Refining twisted bimodules associated to VOAs

TL;DR

This paper refines the structure of bimodules associated with vertex operator algebras by showing a simplification in their defining subspaces, which could impact the understanding of VOA automorphisms.

Contribution

The paper proves that the bimodule $A_{g,n,m}(V)$ can be characterized using only one of the previously defined subspaces, simplifying the structure of these bimodules.

Findings

$O_{g,n,m}(V)$ equals $O_{g,n,m}^{ ext{'}}(V)$

Simplification of bimodule construction

Potential implications for VOA automorphism theory

Abstract

Let $V$ be a vertex operator algebra and $g$ an automorphism of $V$ of finite order $T$. For any $m, n \in(1/T) \mathbb N$, an $A_{g,n}(V)\!-\!A_{g,m}(V)$ bimodule $A_{g,n, m}(V)=V/O_{g,n,m}(V)$ was defined by Dong and Jiang, where $O_{g,n,m}(V)$ is the sum of three certain subspaces $O_{g,n, m}^{\prime}(V), O_{g,n, m}^{\prime \prime}(V)$ and $O_{g,n, m}^{\prime \prime \prime}(V)$. In this paper, we show that $O_{g,n, m}(V)=O_{g,n, m}^{\prime}(V)$.