The Dynkin-Specht-Wever lemma and some associated constructions

TL;DR

This paper extends classical algebraic lemmas and constructions, including the Dynkin-Specht-Wever lemma and Burgunder's splitting, and explores their connections to the Kashiwara-Vergne problem in Lie theory.

Contribution

It introduces new extensions of the Dynkin-Specht-Wever lemma and generalizes Burgunder's splitting construction, linking these to the Kashiwara-Vergne problem.

Findings

Extended the Dynkin-Specht-Wever lemma with new algebraic formulations

Generalized Burgunder's splitting construction

Connected these extensions to the Kashiwara-Vergne problem

Abstract

In the first part of the paper, some extensions of the classical Dynkin-Specht-Wever lemma are developed. In the second part, we extend Burgunder's splitting construction, and relate back to the Kashiwara-Vergne problem.