On universal conformal envelopes for quadratic conformal algebras

TL;DR

This paper proves that all quadratic Lie conformal algebras based on a specific Gelfand-Dorfman algebra can be embedded into a universal associative conformal algebra with a bounded locality function, advancing the understanding of their algebraic structure.

Contribution

It establishes the embedding of quadratic Lie conformal algebras into universal associative conformal algebras with a specific locality bound, providing a new structural insight.

Findings

Embedding of quadratic Lie conformal algebras into universal associative conformal algebras with N=3

Extension of the theory of conformal algebras to include specific Gelfand-Dorfman structures

Clarification of the algebraic relationships and bounds in conformal algebra embeddings

Abstract

We prove that every quadratic Lie conformal algebra constructed on a special Gelfand-Dorfman algebra embeds into the universal enveloping associative conformal algebra with a locality function bound N = 3.