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arXiv · 2308.09052

Linear models of the exceptional Lie algebra $\mathfrak{e}_8$

Yolanda Cabrera·Cristina Draper·Antonio Garvin
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Abstract

This work provides five explicit constructions of the exceptional Lie algebra $\mathfrak{e}_8$, based on its semisimple subalgebras of maximal rank. Each of these models is graded by an abelian group, namely, $\mathbb{Z}_4$, $\mathbb{Z}_5$, $\mathbb{Z}_6$, $\mathbb{Z}_3^2$ and $\mathbb{Z}_2\times\mathbb{Z}_4$; the neutral component is direct sum of special linear algebras and the remaining homogeneous components are irreducible modules for it.

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Yolanda Cabrera, Cristina Draper, Antonio Garvin. 2023-08-17. Linear models of the exceptional Lie algebra $\mathfrak{e}_8$. https://doi.org/10.1007/s13398-025-01768-3

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