Twisted modules and pseudo-endomorphisms

TL;DR

This paper explores the relationship between two methods of constructing twisted modules for vertex operator algebras, focusing on inner automorphisms and pseudo-endomorphisms, and introduces related deformation concepts.

Contribution

It establishes a connection between two existing constructions of twisted modules and investigates pseudo-derivations and pseudo-endomorphisms in this context.

Findings

Connected two constructions of twisted modules for vertex operator algebras.

Studied pseudo-derivations and pseudo-endomorphisms related to twist deformations.

Provided insights into the structure of modules under inner automorphisms.

Abstract

We exhibit a connection between two constructions of twisted modules for a general vertex operator algebra with respect to inner automorphisms. We also study pseudo-derivations, pseudo-endomorphisms, and twist deformations of ordinary modules by pseudo-endomorphisms, which are intrinsically connected to one of the two constructions.