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arXiv · 2606.06422

Free Reductive Lie Algebra Pairs of Lie-Yamaguti algebras

Saïd Benayadii·Martin Bordemann·Friedrich Wagemann
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Abstract

The goal of this article is to show the categorical links between on the one hand the category of reductive Lie algebra pairs $\mathcal{RLP}$ and on the other hand the category of Lie-Yamaguti algebras $\mathcal{LY}$. The fact that the well-known construction of an enveloping algebra associating to a Lie-Yamaguti algebra a reductive Lie algebra pair is not functorial leads us to the main construction of the article, namely a left adjoint to the natural restriction functor $G:\mathcal{RLP}\to\mathcal{LY}$. As a final result we observe that the construction of the enveloping algebra becomes functorial when one restricts the morphisms of the categories $\mathcal{RLP}$ and $\mathcal{LY}$ to the surjective ones. Then it becomes a right adjoint to the restriction functor.

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Saïd Benayadii, Martin Bordemann, Friedrich Wagemann. 2026-06-04. Free Reductive Lie Algebra Pairs of Lie-Yamaguti algebras. https://arxiv.org/abs/2606.06422

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