Toward a Jacobson--Morozov theorem for Kac--Moody Lie algebras

Sam Jeralds

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arXiv · 2108.01120

Toward a Jacobson--Morozov theorem for Kac--Moody Lie algebras

Sam Jeralds

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Abstract

For a finite-dimensional semisimple Lie algebra $\mathfrak{g}$, the Jacobson--Morozov theorem gives a construction of subalgebras $\mathfrak{sl}_2 \subset \mathfrak{g}$ corresponding to nilpotent elements of $\mathfrak{g}$. In this note, we propose an extension of the Jacobson--Morozov theorem to the symmetrizable Kac--Moody setting and give a proof of this generalization in the case of rank two hyperbolic Kac--Moody algebras. We also give a proof for an arbitrary symmetrizable Kac--Moody algebra under some stronger restrictions.

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Sam Jeralds. 2021-08-02. Toward a Jacobson--Morozov theorem for Kac--Moody Lie algebras. https://arxiv.org/abs/2108.01120

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