2-Recognizeable Classes of Leibniz Algebras

TL;DR

This paper demonstrates that specific classes of Leibniz algebras, including solvable, strongly solvable, and super solvable, are 2-recognizeable over certain fields, extending known results from Lie algebras and groups.

Contribution

It establishes the 2-recognizeability of key classes of Leibniz algebras over fields with characteristic 0 or >5, generalizing previous Lie algebra and group results.

Findings

Solvable Leibniz algebras are 2-recognizeable over specified fields.

Strongly solvable Leibniz algebras are 2-recognizeable.

Super solvable Leibniz algebras are 2-recognizeable.

Abstract

We show that for fields that are of characteristic 0 or algebraically closed of characteristic greater than 5, that certain classes of Leibniz algebras are 2-recognizeable. These classes are solvable, strongly solvable and super solvable. These results hold in Lie algebras and in general for groups.