Simplicity of quadratic Lie conformal algebras

TL;DR

This paper investigates the simplicity conditions of quadratic Lie conformal algebras, providing criteria and constructing new classes of infinite simple Lie conformal algebras to aid classification efforts.

Contribution

It offers new necessary and sufficient conditions for simplicity and introduces several new classes of infinite simple Lie conformal algebras.

Findings

Established criteria for simplicity of quadratic Lie conformal algebras

Presented new classes of infinite simple Lie conformal algebras

Provided tools for classification of Lie conformal algebras

Abstract

In this paper, simplicity of quadratic Lie conformal algebras are investigated. From the point view of the corresponding Gel'fand-Dorfman bialgebras, some sufficient conditions and necessary conditions to ensure simplicity of quadratic Lie conformal algebras are presented. By these observations, we present several classes of new infinite simple Lie conformal algebras. These results will be useful for classification purposes.