Conjugacy of Cartan Subalgebras in Solvable Leibniz Algebras and Real Leibniz Algebras

TL;DR

This paper extends conjugacy results of Cartan subalgebras from Lie algebras to solvable Leibniz algebras, overcoming challenges posed by the lack of anti-commutativity, and demonstrates applications of these results.

Contribution

It introduces new conjugacy results for Cartan subalgebras in solvable Leibniz algebras, generalizing Lie algebra theory.

Findings

Conjugacy results for Cartan subalgebras in Leibniz algebras.

Methods to overcome anti-commutativity dependence.

Examples illustrating the extended results.

Abstract

We extend conjugacy results from Lie algebras to their Leibniz algebra generalizations. The proofs in the Lie case depend on anti-commutativity. Thus it is necessary to find other paths in the Leibniz case. Some of these results involve Cartan subalgebras. Our results can be used to extend other results on Cartan subalgebras. We show an example here and others will be shown in future work.