On embedding of Lie conformal algebras into associative conformal algebras
Michael Roitman

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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons
