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.

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.