On the Ado Theorem for finite Lie conformal algebras with Levi decomposition

TL;DR

This paper proves that finite torsion-free conformal Lie algebras with Levi decomposition possess finite faithful conformal representations, advancing understanding of their structure and representation theory.

Contribution

It establishes the existence of finite faithful conformal representations for a class of finite torsion-free conformal Lie algebras with Levi decomposition, which was previously unknown.

Findings

Finite torsion-free conformal Lie algebras with Levi decomposition have finite faithful conformal representations.

The result extends the Ado theorem to a broader class of conformal Lie algebras.

The proof relies on the structure theory of conformal Lie algebras with Levi decomposition.

Abstract

We prove that a finite torsion-free conformal Lie algebra with a splitting solvable radical has a finite faithful conformal representation.