On embedding of Lie conformal algebras into associative conformal algebras

TL;DR

This paper proves that Lie conformal algebras with bounded locality can be embedded into associative conformal algebras with preserved properties, including nilpotency, and discusses open questions in the field.

Contribution

It establishes an embedding theorem for Lie conformal algebras into associative conformal algebras, preserving bounded locality and nilpotency, and explores related open problems.

Findings

Lie conformal algebras with bounded locality are embeddable into associative conformal algebras

Nilpotent Lie conformal algebras embed into nilpotent associative conformal algebras with the same nilpotency index

The paper presents open questions on embeddings of Lie conformal algebras

Abstract

We prove that a Lie conformal algebra L with bounded locality function is embeddable into an associative conformal algebra A with the same bound on the locality function. If L is nilpotent, then so is A, and the nilpotency index remains the same. We also give a list of open questions concerning the embedding of Lie conformal algebras into associative conformal.