Twisted associative algebras associated to vertex algebras

TL;DR

This paper constructs a sequence of associative algebras linked to vertex algebras with automorphisms, demonstrating that certain properties of vertex operator algebras are independent of their conformal structure.

Contribution

It introduces a new family of associative algebras associated to vertex algebras with automorphisms, independent of conformal structure, and explores their implications.

Findings

Constructed associative algebras $ ilde{A}_{g,n}(V)$ for vertex algebras.

Showed $g$-rationality and $g$-regularity are conformal vector independent.

Established twisted fusion rules are independent of conformal vector choice.

Abstract

Let $V$ be a vertex algebra and $g$ an automorphism of $V$ of order $T$. We construct a sequence of associative algebras $\tilde{A}_{g,n}(V )$ for any $n\in(1/T)\mathbb{N}$, which are not depend on the conformal structure of $V$. We show that for a vertex operator algebra, $g$-rationality, $g$-regularity, and twisted fusion rules are independent of the choice of the conformal vector.