Induced modules for vertex operator algebras

TL;DR

This paper introduces a new $g$-twisted induction functor for modules over vertex operator algebras, satisfying key properties like Frobenius reciprocity, and explores its applications in specific algebraic contexts.

Contribution

It develops a novel $g$-twisted induction functor for modules of vertex operator algebras, extending module theory under automorphisms.

Findings

The functor satisfies Frobenius reciprocity.

The functor exhibits transitivity.

Applications include simple $V$ and $g$-rational $V'$ cases.

Abstract

For a vertex operator algebra $V$ and a vertex operator subalgebra $V'$ which is invarinant under an automorphism $g$ of $V$ of finite order, we introduce a $g$-twisted induction functor from the category of $g$-twisted $V'$-modules to the category of $g$-twisted $V$-modules. This functor satisfies the Frobenius reciprocity and transitivity. The results are illustrated with $V$ being simple or with $V'$ being $g$-rational.