# Locally finite admissible simple Lie algebras

## TL;DR

This paper introduces admissible Lie algebras, a new class of locally finite simple Lie algebras, and demonstrates their structural properties including the existence of maximal toral subalgebras and irreducible root systems.

## Contribution

The paper defines admissible Lie algebras and establishes their key structural features, expanding the understanding of locally finite simple Lie algebra classifications.

## Key findings

- Existence of nonzero maximal toral subalgebras in admissible Lie algebras
- Root systems are irreducible and locally finite
- Structural characterization of admissible Lie algebras

## Abstract

We introduce a class of Lie algebras called admissible Lie algebras. We show that a locally finite admissible simple Lie algebra contains a nonzero maximal toral subalgebra and the corresponding root system is an irreducible locally finite root system.