On minimal non-elementary Lie algebras

TL;DR

This paper classifies minimal non-elementary Lie algebras over algebraically closed fields with characteristic not 2 or 3, and characterizes solvable cases over any perfect field, advancing understanding of their structure.

Contribution

It provides a complete classification of minimal non-elementary Lie algebras under specific field conditions and characterizes solvable instances over perfect fields, filling gaps in Lie algebra theory.

Findings

Classified minimal non-elementary Lie algebras over algebraically closed fields of characteristic ≠ 2,3

Characterized solvable minimal non-elementary Lie algebras over perfect fields

Extended structural understanding of these Lie algebras

Abstract

The class of minimal non-elementary Lie algebras over a field F are studied. These are classified when F is algebraically closed and of characteristic different from 2,3. The solvable algebras in this class are also characterised over any perfect field.