Finite vertex algebras and nilpotence

TL;DR

This paper proves that simple finite vertex algebras are commutative and that their underlying Lie conformal algebra structures are nilpotent, revealing fundamental structural properties of these algebraic objects.

Contribution

It establishes that simple finite vertex algebras are commutative and their associated Lie conformal algebras are nilpotent, providing new insights into their algebraic structure.

Findings

Simple finite vertex algebras are commutative.

Underlying Lie conformal algebras of reduced finite vertex algebras are nilpotent.

Structural properties of finite vertex algebras are clarified.

Abstract

I show that simple finite vertex algebras are commutative, and that the Lie conformal algebra structure underlying a reduced (i.e., without nilpotent elements) finite vertex algebra is nilpotent.