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arXiv · 2508.02245

Graded contractions of the $\mathbb{Z}_2^3$-gradings on the exceptional Lie algebras coming from octonions

Francisco Cuenca·Cristina Draper·Thomas L. Meyer
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Abstract

A total of 860 nonisomorphic \( \mathbb{Z}_2^3 \)-graded Lie algebras of dimensions 52, 78, 133, and 248 are obtained as graded contractions of the \( \mathbb{Z}_2^3 \)-gradings on the exceptional Lie algebras (excluding \( \mathfrak{g}_2 \)) arising from the octonions. It is shown that all graded contractions of these gradings are necessarily generic. Their supports correspond to a combinatorial object known as a \emph{generalised nice set}, which serves as the main tool in the classification. The resulting algebras are distinguished by their Levi decompositions, the derived series of their radicals, their centers, and other structural features.

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Francisco Cuenca, Cristina Draper, Thomas L. Meyer. 2025-08-04. Graded contractions of the $\mathbb{Z}_2^3$-gradings on the exceptional Lie algebras coming from octonions. https://arxiv.org/abs/2508.02245

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