Ordered spanning sets for quasimodules for Mobius vertex algebras

TL;DR

This paper extends the theory of spanning sets to quasimodules for Mobius vertex algebras, providing new structured bases that generalize existing module spanning set results.

Contribution

It introduces two new spanning set constructions for quasimodules, broadening the understanding of their algebraic structure within Mobius vertex algebras.

Findings

Two new spanning sets with difference-zero and difference-one conditions

Generalization of spanning set results to quasimodules for Mobius vertex algebras

Bridges module theory and twisted module theory through these spanning sets

Abstract

Quasimodules for vertex algebras are generalizations of modules for vertex algebras. These new objects arise from a generalization of locality for fields. Quasimodules tie together module theory and twisted module theory, and both twisted and untwisted modules feature Poincare-Birkhoff-Witt-like spanning sets. This paper generalizes these spanning set results to quasimodules for certain Mobius vertex algebras. In particular this paper presents two spanning sets, one featuring a difference-zero ordering restriction on modes and another featuring a difference-one condition.