Spanning sets for Moebius vertex algebras satisfying arbitrary difference conditions

TL;DR

This paper generalizes spanning set results for Moebius vertex algebras, demonstrating that with an appropriate generating set, these algebras are spanned by monomials adhering to a difference-N ordering condition.

Contribution

It extends previous work on difference-zero and difference-one conditions to arbitrary difference-N conditions for Moebius vertex algebras.

Findings

Established spanning sets for N-graded Moebius vertex algebras with difference-N conditions.

Unified the understanding of spanning sets across various difference conditions.

Provided a framework for constructing bases with difference-N ordering constraints.

Abstract

Spanning sets for vertex operator algebras satisfying difference-zero and difference-one conditions have been extensively studied in the recent years. In this paper, we extend these results. More specifically, we show that for a suitably chosen generating set, any N-graded Moebius vertex algebra is spanned by monomials satisfying a difference-N ordering condition.