On quasi modules at infinity for vertex algebras

TL;DR

This paper revisits the theory of quasi modules at infinity for vertex algebras, extending previous results, filling gaps in proofs, and establishing new formulas and theorems to deepen understanding of their structure.

Contribution

It extends technical results on quasi modules at infinity for vertex algebras, fills a proof gap, and derives a new commutator formula and a converse theorem.

Findings

Extended theorems for quasi modules at infinity.

Provided a new commutator formula.

Established a converse of a key theorem.

Abstract

A theory of quasi modules at infinity for (weak) quantum vertex algebras including vertex algebras was previously developed in \cite{li-infinity}. In this current paper, quasi modules at infinity for vertex algebras are revisited. Among the main results, we extend some technical results, to fill in a gap in the proof of a theorem therein, and we obtain a commutator formula for general quasi modules at infinity and establish a version of the converse of the aforementioned theorem.