The subalgebras of $A_2$

TL;DR

This paper completes the classification of all subalgebras of the Lie algebra $A_2$ by including the nonsemisimple cases, which were previously unclassified.

Contribution

It provides a comprehensive classification of nonsemisimple subalgebras of $A_2$, extending the known semisimple subalgebra classification.

Findings

Complete classification of subalgebras of $A_2$

Identification of nonsemisimple subalgebras

Extension of existing classification results

Abstract

A classification of the semisimple subalgebras of the Lie algebra of traceless $3\times 3$ matrices with complex entries, denoted $A_2$, is well-known. We classify its nonsemisimple subalgebras, thus completing the classification of the subalgebras of $A_2$.