Graded contractions of the $\mathbb{Z}_2^3$-gradings on the exceptional Lie algebras coming from octonions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913974445932544 |
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| author | Cuenca, Francisco Draper, Cristina Meyer, Thomas L. |
| author_facet | Cuenca, Francisco Draper, Cristina Meyer, Thomas L. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_02245 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Graded contractions of the $\mathbb{Z}_2^3$-gradings on the exceptional Lie algebras coming from octonions Cuenca, Francisco Draper, Cristina Meyer, Thomas L. Rings and Algebras 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. |
| title | Graded contractions of the $\mathbb{Z}_2^3$-gradings on the exceptional Lie algebras coming from octonions |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2508.02245 |